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\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \begin{thebibliography}{100} \bibitem{abdes} B.~Abdesselam, J.~Beckers, A.~Chakabarti, and N.~Debergh, \emph{On a deformation of {$sl(2)$} with paragrassmanian variables}, J. Phys. A: Math. Gen. \textbf{29} (1996), 6729--6736. \bibitem{adjan_book} S.~I. Adian, \emph{The {B}urnside problem and identities in groups}, Ergebnisse der Math. und ihrer Grenzbebeite, vol.~95, Springer, Berlin, 1979, Transl. from Russian edn.: Nauka, Moscow, 1975. \bibitem{akhi_book} N.~I. Akhiezer, \emph{Classical moment problem}, Oliver and Boyd, 1965, Transl. from Russian edn: Fizmatgiz, Moscow, 1961. \bibitem{akh_glaz} N.~I. Akhiezer and I.~M. Glazman, \emph{The theory of linear operators in {H}ilbert space}, Ungar, New York, 1961, Transl. from Russian edn.: Gostekhizdat, Moscow, 1950. \bibitem{126} S.~A. Amitsur and J.~Levitski, \emph{Minimal identities for algebras}, Proc. Amer. Math. Soc. \textbf{1} (1950), 449--463. \bibitem{araki60} H.~Araki, \emph{Hamiltonian formalism and canonical relations in quantum field theory}, J. Math. Phys. \textbf{1} (1960), no.~4, 492--504. \bibitem{54} R.~Arens, \emph{Representations of $*$-algebras}, Duke Math. J. \textbf{14} (1947), 269--282. \bibitem{56} W.~B. Arveson, \emph{Operator algebras and invariant subspaces}, Ann Math. \textbf{100} (1974), 433--532. \bibitem{arv76} \bysame, \emph{An invitation to {$C^*$}-algebras}, Graduate texts in mathematics, vol.~39, Springer, Berlin, 1976. \bibitem{13} \bysame, \emph{The harmonic analysis of automorphism groups}, Proc. Symp. Pure Math. \textbf{38} (1982), 199--269. \bibitem{arv89} \bysame, \emph{Continuous analogues of {F}ock space}, Mem. Amer. Math. Soc., vol.~80, Amer. Math. Soc., Providence, R.I., 1989. \bibitem{arz_ver2} V.~Arzumanian and A.~Vershik, \emph{Star-algebras associated with endomorphisms}, Operator algebras and group representations, Proc Int. Conf., vol. I. (Boston), Pitman, 1984, pp.~17--27. \bibitem{aus} M.~Auslander, I.~Reiten, and S.~O. Smalo, \emph{Representation theory of {A}rtin algebras}, Cambridge studies in advanced mathematics, vol.~36, Cambridge Univ. Press, 1995. \bibitem{azi_io} T.~Ya. Azizov and I.~S. Iohvidov, \emph{Linear operators in spaces with an indefinite mertic}, J. Wiley and Sons, New York, 1989, Transl. from Russian edn.: Nauka, Moscow, 1986. \bibitem{90} O.~V. Bagro, \emph{Pairs of self-adjoint operators connected by a cubic relation}, Ukrain. Mat. Zh. \textbf{47} (1995), no.~5, 600--602, (Russian). \bibitem{bagro_kru_2} O.~V. Bagro and S.~A. Kruglyak, \emph{Representations of involutive quivers and wild problems}, Preprint KVIUS, Kiev, 1995, (Russian). \bibitem{bagro_kru} \bysame, \emph{Representations of {D}. {F}airlie algebras}, Preprint KVIUS, Kiev, 1996, (Russian). \bibitem{barn} B.~A. Barnes, \emph{A note on separating families of representations}, Proc. Amer. Math. Soc. \textbf{87} (1983), 95--98. \bibitem{bart} H.~Bart, T.~Ehrhardt, and B.~Silbermann, \emph{Zero sums of idempotents in {B}anach algebras}, Integr. Equat. Oper. Theory \textbf{19} (1994), 125--134. \bibitem{59} A.~O. Barut and R.~Raczka, \emph{Theory of group representations and applications}, PWN, Warszawa, 1977. \bibitem{benk} H.~Bencke, \emph{Generators of {$W^*$}-algebras}, Tohoku Math. J. \textbf{22} (1970), 541--546. \bibitem{benk_ii} \bysame, \emph{Generators of {$W^*$}-algebras {II}}, Tohoku Math. J. \textbf{24} (1972), 371--381. \bibitem{benk_iii} \bysame, \emph{Generators of {$W^*$}-algebras {III}}, Tohoku Math. J. \textbf{24} (1972), 383--388. \bibitem{ber0} Yu.~M. Berezansky, \emph{Expansion in eigenfunctions of selfadjoint operators}, Transl. Math. Monogr., vol.~17, Amer. Math. Soc., Providence, R.I., 1968, Transl. from Russian edn.: Naukova Dumka, Kiev, 1965. \bibitem{ber1} \bysame, \emph{Self-adjoint operators in spaces of functions of infinitely many variables}, Trans. Math. Monographs, vol.~63, AMS, Providence, R.I., 1986, Transl. from Russian edn.: Kiev, Naukova Dumka, 1978. \bibitem{berkon} Yu.~M. Berezansky and Yu.~G. Kondrat'ev, \emph{Spectral methods in infinite dimensional analysis}, Kluwer Acad. Publ., Dordrecht, 1992, Transl. from Russian edn.: Naukova Dumka, Kiev, 1988. \bibitem{65} Yu.~M. Berezansky, G.~Lassner, and V.~S. Yakovlev, \emph{On decomposition of positive functionals on commutative nuclear $*$-algebras}, Ukrain. Mat. Zhurn. \textbf{39} (1987), no.~5, 638--641, (Russian). \bibitem{bos} Yu.~M. Berezansky, V.~L. Ostrovsky\u\i{}, and Yu.~S. Samo\u\i{}lenko, \emph{Eigenfunction expansion of families of commuting operators and representations of commutation relations}, Ukr. Math. Zh. \textbf{40} (1988), no.~1, 106--109, (Russian). \bibitem{ber_us_sh} Yu.~M. Berezansky, Z.~G. Sheftel, and G.~F. Us, \emph{Functional analysis {I}, {II}}, Operator Theory, Adv. Appl., vol. 85, 86, Birkh\"auser Verlag, Basel, 1996, Transl. from Russian edn.: Vyshcha Shkola, Kiev, 1990. \bibitem{68} F.~A. Berezin and G.~I. Kats, \emph{Lie groups with commuting and anticommuting parameters}, Matem. Sbornik \textbf{82} (1970), no.~3, 343--359, (Russian). \bibitem{berg_cob_leb} C.~A. Berger, L.~A. Coburn, and A.~Lebow, \emph{Representation and index theory for ${C}^*$-algebras generated by commuting isometries}, J. Funct. Anal. \textbf{27} (1978), 51--99. \bibitem{besp_umz} Yu.~N. Bespalov, \emph{Collections of orthoprojections satisfying relations}, Ukr. Mat. Zhurn. \textbf{44} (1992), no.~3, 309--317, (Russian). \bibitem{besp_mfat} \bysame, \emph{Algebraic operators, partial isometries, and wild problems}, Methods Funct. Anal. Topol. \textbf{3} (1997), no.~1, 28--45. \bibitem{bessam1} Yu.~N. Bespalov and Yu.~S. Samo\u\i{}lenko, \emph{Algebraic operators and pairs of selfadjoint operators connected by a polynomial relation}, Funct. Anal. i Prilozhen. \textbf{25} (1991), no.~4, 72--74, (Russian). \bibitem{bss} Yu.~N. Bespalov, Yu.~S. Samo\u\i{}lenko, and V.~S. Shul'man, \emph{On families of operators connected by semi-linear relations}, Applications of Methods of Functional Analysis in Mathematical Physics, Inst. Math. Acad. Sci. Ukraine, Kiev, 1991, (Russian), pp.~28--51. \bibitem{biede} L.~C. Biedenharn, \emph{The quantum group $su_q(2)$ and a $q$-analogue of the boson operators}, J. Phys. A \textbf{22} (1989), L873--L878. \bibitem{69} M.~Sh. Birman and M.~A. Solomyak, \emph{The spectral theory of self-adjoint operators in {H}ilbert space}, Izdat. Leningrad. Univ, Leningrad, 1980. \bibitem{black} B.~E. Blackadar, \emph{A simple unital projectionless {$C^*$}-algebra}, J. Oper. Theory \textbf{5} (1981), 63--71. \bibitem{bon_dr} V.~M. Bondarenko and Yu.~A. Drozd, \emph{Representations type of finite groups}, Zap. Nauchn. Sem. LOMI \textbf{71} (1977), 24--42, (Russian). \bibitem{116} A.~B{\"o}ttcher, I.~Gohberg, Yu. Karlovich, N.~Krupnik, S.~Roch, B.~Silberman, and I.~Spitkovsky, \emph{Banach algebras generated by {$N$} idempotents and applications}, Operator Theory Adv. Appl. \textbf{90} (1996), 19--54. \bibitem{121} N.~Bourbaki, \emph{Groupes et algebres de {L}ie {IV--VI}}, Hemmann, Paris, 1968. \bibitem{boz_sp91} M.~Bo\.zejko and R.~Speicher, \emph{An example of a generalized {B}rownian motion.}, Commun. Math. Phys. \textbf{37} (1991), 519--531. \bibitem{102} M.~Bo\.zejko and R.~Speicher, \emph{Completely positive maps on {C}oxeter groups, deformed commutation relations, and operator spaces}, Math. Ann. \textbf{300} (1994), 97--120. \bibitem{bra_jor2} O.~Bratteli and P.~E.~T. J\o{}rgensen, \emph{Endomorphisms of {$\mathcal B(\mathcal H)$}. {II}. {F}initely correlated states on {$\mathcal{O}_n$}}, J. Funct. Anal. \textbf{145} (1997), no.~2, 323--373. \bibitem{jor} \bysame, \emph{Isometries, shifts, {C}untz algebras and multiresolution wavelet analysis of scale {$N$}}, Int. Equat. Oper. Theory \textbf{28} (1997), 382--443. \bibitem{brat-jorg} O.~Bratteli and P.~E.~T. J\o{}rgensen, \emph{Iterated function systems and permutation representations of the {C}untz algebra}, Mem. Amer. Math. Soc., AMS, 1998. \bibitem{bra_jor1} O.~Bratteli, P.~E.~T. J\o{}rgensen, and G.~L. Price, \emph{Endomorphisms of {$\mathcal B(\mathcal H)$}}, Proc. Symp. Pure Math. \textbf{59} (1996), 93--138. \bibitem{70} O.~Bratteli and D.~W. Robinson, \emph{Operator algebras and quantum statistical mechanics}, Books and Monographs in Physics, Springer-Velag, 1979. \bibitem{91} A.~Brown, \emph{On a class of operators}, Proc Amer. Math. Soc. \textbf{4} (1953), 723--728. \bibitem{brown} \bysame, \emph{The unitary equivalence of binormal operators}, Amer. J. Math. \textbf{76} (1954), no.~2, 414--434. \bibitem{43} L.~Brown, P.~Green, and M.~A. Rieffel, \emph{Stable isomorphism ans strong {M}orita eqivalence of {$C^*$}-algebras}, Pacific J. Math. \textbf{71} (1977), 349--363. \bibitem{bukl2} I.~M. Burban and A.~U. Klimyk, \emph{On spectral properties of $q$-oscillator operators}, Lett. Math. Phys. \textbf{29} (1993), 13--18. \bibitem{camp} S.~L. Campbell, \emph{Linear operators for which {$T^*T$} and {$TT^*$} commute ({II})}, Pacific Journ. Math. \textbf{53} (1974), no.~2, 355--361. \bibitem{chari} V.~Chari and A.~N. Pressly, \emph{A guide to quantum groups}, Cambridge Univ. Press, Cambridge, 1994. \bibitem{21} M.~D. Choi, \emph{The full {$C^*$}-algebra of the free group of two generators}, Pacific J. Math. \textbf{87} (1980), no.~1, 41--48. \bibitem{29} J.~M. Cohen, \emph{{$C^*$}-algebras without idempotents}, J. Funct. Anal. \textbf{33} (1979), 211--216. \bibitem{conn} A.~Connes, \emph{Non-commutative geometry}, Acad. Press, New York, 1994. \bibitem{cuntz} J.~Cuntz, \emph{Simple ${C}^*$-algebras generated by isometries}, Commun. Math. Phys. \textbf{57} (1977), 173--185. \bibitem{cur_re} Ch.~W. Curtis and I.~Reiner, \emph{Representation theory of finite groups and associative algebras}, Wiley, New York, 1962. \bibitem{dal} Yu.~L. Daletski\u\i{}, \emph{Functional integrals related with operator evolution equations}, Uspekhi Mat. Nauk \textbf{17} (1962), no.~5, 3--115, (Russian). \bibitem{73} A.~Yu. Daletsky and Yu.~S. Samo\u\i{}lenko, \emph{A noncommutative moment problem}, Funts. Anal. Prilozh. \textbf{21} (1987), no.~2, 72--73, (Russian). \bibitem{damku} E.~V. Damaskinsky and P.~P. Kulish, \emph{Deformed oscillators and their applications}, Zap. Nauchn. Sem. LOMI \textbf{189} (1991), 37--74, (Russian). \bibitem{greek} C.~Daskaloyanis, \emph{Generalized deformed oscillator and nonlinear algebras}, J. Phys. A \textbf{24} (1991), L789--L794. \bibitem{34} K.~R. Davidson, \emph{{$C^*$}-algebras by example}, Amer. Math. Soc., Providence, R.I., 1997. \bibitem{111} C.~Davis, \emph{Separation of two linear subspaces}, Acta Sci. Math. Szeged \textbf{19} (1958), 172--187. \bibitem{quesne3} C.~Delbecq and C.~Quesne, \emph{A cubic deformation of $su(2)$}, Modern Phys. Lett. A \textbf{8} (1993), 961--966. \bibitem{quesne} \bysame, \emph{Representation theory and $q$-boson realizations of {W}itten's $su(2)$ and $su(1,1)$ deformations}, Phys. Lett. B \textbf{300} (1993), 227--233. \bibitem{78} J.~Dixmier, \emph{Les {$C^*$}-algebras et leur representations}, Gauthier-Villars, Paris, 1969. \bibitem{112} D.~\v{Z}. Dokovi\v{c}, \emph{Unitary similarity of projectors}, Aequationes Math. \textbf{42} (1991), 220--224. \bibitem{89} P.~Donovan and M.~R. Freislich, \emph{Some evidence for an extension of the {B}rauer--{T}hrall conjecture}, Sonderforschungsbereich Theor. Math. \textbf{40} (1972), 24--26. \bibitem{dor_bel} R.~S. Doran and V.~A. Belfi, \emph{Characterization of {$C^*$}-algebras. {T}he {G}elfand--{N}aimark theorems}, Pure and applied mathematics, vol. 101, Marcel Dekker, Inc., New York, Basel, 1986. \bibitem{douglas} R.~G. Douglas, \emph{Banach algebra techniques in operator theory}, Acad. Press, New York, London, 1972. \bibitem{drinf} V.~G. Drinfeld, \emph{Hopf algebras and the quantum {Y}ang--{B}axter equation}, Soviet Math. Dokl. \textbf{32} (1985), no.~1, 254--258. \bibitem{drozd} Yu.~A. Drozd, \emph{Tame and wild matrix problems}, Representations and quadratic forms, Inst. Mat. AN UkrSSR, Kiev, 1979, pp.~39--74, (Russian). \bibitem{dye} H.~A. Dye, \emph{On groups of measure preserving transformations. {I}}, Amer. J. Math. \textbf{81} (1959), 119--159. \bibitem{dyk_nica} K.~Dykema and A.~Nica, \emph{On the {F}ock representation of the $q$-commutation relations}, J. Reine Angew. Math. \textbf{440} (1993), 201--212. \bibitem{efr} E.~G. Effros and F.~Hahn, \emph{Locally compact transformation groups and {$C^*$}-algebras}, Mem. Amer. Math. Soc, vol.~75, Amer. Math. Soc., Providence, R.I., 1967. \bibitem{7} G.~G. Emch, \emph{Algebraic methods in statistical mechanics and quantum field theory}, Wiley--Interscience, 1972. \bibitem{ern} J.~Ernest, \emph{Charting the operator terrain}, Mem. Amer. Math. Soc., vol. 171, Amer. Math. Soc., Providence, R.I., 1976. \bibitem{fai} D.~B. Fairlie, \emph{Quantum deformations of {$SU(2)$}}, J. Phys. A: Math. and Gen. \textbf{23} (1990), L183--L186. \bibitem{finck} T.~Finck, S.~Roch, and B.~Silbermann, \emph{Two projections theorems and symbol calculus for operators with massive local spectra}, Math. Nachr. \textbf{162} (1993), 167--185. \bibitem{flato} M.~Flato, J.~Simon, H.~Snellman, and D.~Sternheimer, \emph{Simple facts about analytic vectors and integrability}, Ann. Scient. de l'\'Ecole Norm. Sup. \textbf{5} (1972), 423--434. \bibitem{16} M.~Fragoulopulou, \emph{An introduction to the representation theory of topological $*$-algebras}, Schriftenreihne des Math. Inst. der Univ. M{\"u}nster, vol.~48, Univ. M\"unster, 1988. \bibitem{gar_w_car} L.~G\aa{}rding and A.~Wightman, \emph{Representations of the anticommutation relations}, Proc. Nat. Acad. Sci. USA \textbf{40} (1954), no.~9, 617--622. \bibitem{gar_w_ccr} \bysame, \emph{Representations of the commutation relations}, Proc. Nat. Acad. Sci. USA \textbf{40} (1954), no.~9, 623--626. \bibitem{gab_roi_book} P.~Gabriel and A.~V. Roiter, \emph{Representations of finite-dimensional algebras}, Springer-Verlag, Berlin, 1997. \bibitem{117} P.~Gabriel and M.~Zisman, \emph{Calculus of fractions and homotopy theory}, Springer, Berlin--Heidelberg--New York, 1967. \bibitem{gal_mfat} D.~V. Galinsky, \emph{Representations of $*$-algebras generated by orthogonal projections satisfying a linear relation}, Methods Funct. Anal. Topol. \textbf{4} (1998), no.~3, 27--32. \bibitem{gal_mur} D.~V. Galinsky and M.~A. Muratov, \emph{On representations of algebras generated by sets of three and four orthoprojections}, Spectral and evolutionary problems. vol. 8, Tavria, Simferopol, 1998, pp.~15--22. \bibitem{139} O.~M. Gavrilik and A.~U. Klimyk, \emph{Representations of the {$q$}-deformed algebras {$U_q(so_{2,1})$}, {$U_q(so_{3,1})$}}, J. Math. Phys. \textbf{35} (1994), no.~2, 3670--3686. \bibitem{gelpon} I.~M. Gel'fand and V.~A. Ponomarev, \emph{Remarks on classification of a pair of commuting linear transformations in a finite-dimensional space}, Funct. Anal. i Prilozh. \textbf{3} (1969), no.~4, 81--82, (Russian). \bibitem{127} I.~M. Gel'fand and V.~A. Ponomarev, \emph{Quadruples of subspaces of a finite-dimensional vector space}, Dokl. Akad. Nauk SSSR \textbf{197} (1971), no.~4, 762--765, (Russian). \bibitem{gel} I.~M. Gelfand and N.~Ya. Vilenkin, \emph{Generalized functions}, vol.~4, Academic Press, New York, 1964, Transl. from Russian edn.: Fizmatgiz, Moscow, 1961. \bibitem{gli} J.~Glimm, \emph{A {S}tone--{W}eirstrass theorem for {$C^*$}-algebras}, Ann. Math. \textbf{72} (1960), 216--144. \bibitem{goh_etal} I.~Gohberg, P.~Lancaster, and L.~Rodman, \emph{Matrices and indefinite scalar products}, Oper. Theory Adv. Appl., vol.~8, Birkhauser Verlag, 1983. \bibitem{goh_rei} I.~Gohberg and B.~Reichstein, \emph{On classification of normal matrices in an indefinite scalar product}, Integral Equat. Oper. Theory \textbf{13} (1990), 365--394. \bibitem{goldin} G.~A. Goldin, R.~Menikoff, and D.~H. Sharp, \emph{Particle statistics from induced representations of a local current group}, J. Math. Phys. \textbf{21} (1980), no.~4, 650--664. \bibitem{gol} V.~Ya. Golodets, \emph{Classification of representations of the anticommutation relations}, Russ. Math. Surveys \textbf{24} (1969), 1--63. \bibitem{19} K.~R. Goodearl and P.~Menal, \emph{Free and residually finite-dimensional {$C^*$}-algebras}, J. Funct. Anal. \textbf{9} (1990), no.~2, 391--410. \bibitem{goodman} R.~W. Goodman, \emph{Analytic and entire vectors for representations of {L}ie groups}, Trans. Amer. Math. Soc. \textbf{143} (1969), 55--76. \bibitem{gorpod} M.~F. Gorodni\u\i{} and G.~B. Podkolzin, \emph{Irreducible representations of a graded {L}ie algebra}, Spectral Theory of Operators and Infinite-dimensional Analysis, Inst. Math. Acad. Sci. UkrSSR, Kiev, 1984, pp.~66--76, (Russian). \bibitem{halm2} P.~Halmos, \emph{A {H}ilbert space problem book}, Van Nostrand, Princeton, 1967. \bibitem{halm1} \bysame, \emph{Two subspaces}, Trans. Amer. Math. Soc. \textbf{144} (1969), 381--389. \bibitem{halm_mac} P.~R. Halmos and J.~E. McLaughlin, \emph{Partial isometries}, Pacific J. Math. \textbf{13} (1963), 585--596. \bibitem{77} P. de~la Harpe, \emph{Operator algebras, free groups and other groups}, Recent advances in operator algebras, Orl\'eans, 1992, Asterisque, vol. 232, Soc. Math. France, 1995, pp.~121--153. \bibitem{76} \bysame, \emph{Topics on geometric group theory}, Preliminary version, 1998, http://www.unige.ch/math/biblio/preprint/1998/geogroup/. \bibitem{107} M.~Havli\v{c}ek, A.~U. Klimyk, and E.~Pelantov\'a, \emph{Fairlie algebra {$U_q'(so_3)$}: oscillator realizations, root of unity, reduction {$U_q(sl_3) \supset U_q'(so_3)$}}, Czech J. Phys. \textbf{47} (1997), no.~13. \bibitem{108} M.~Havli\v{c}ek, A.~U. Klimyk, and S.~Po\v{s}ta, \emph{Representations of the cyclically symmetric $q$-deformed algebra $so_q(3)$}, J. Math. Phys. \textbf{40} (1999), 1365--1382. \bibitem{heb_etal} A.~Hebecker, S.~Schreckenberg, J.~Schwenk, W.~Weich, and J.~Wess, \emph{Representations of a {$q$}-deformed {H}eisenberg algebra}, Z. Phys. C \textbf{64} (1994), 355--359. \bibitem{heg_mel} G.~C. Hegerfeldt and O.~Melsheimer, \emph{The form of representations of {CCR} for {B}ose fields and connection with finitely many degrees of freedom}, Commun. Math. Phys. \textbf{12} (1969), no.~4, 304--323. \bibitem{31} I.~Hernstein, \emph{Noncommutative rings}, Math. Assoc. Amer., Wiley, New York, 1968. \bibitem{holevo} A.~S. Holevo, \emph{Probabilistic and staistical aspects of quantum theory}, Nauka, Moscow, 1980, (Russian). \bibitem{113} Kh.~D. Ikramov, \emph{On a canonical form of projections with respect to a unitary similarity}, Zhurn. Vychisl. Mat. i Matem. Fiziki \textbf{36} (1980), no.~1, 3--5, (Russian). \bibitem{inoue} A.~Inoue, \emph{Locally {$C^*$}-algebras}, Mem. Faculty Sci. Kyushu Univ. (Ser. A.) \textbf{25} (1971), 197--235. \bibitem{isma} R.~S. Ismagilov, \emph{Representations of infinite-dimensional groups}, Transl. Math. Monogr., vol. 152, Amer. Math. Soc., Providence, R.I., 1996. \bibitem{32} N.~Jacobson, \emph{Structure of rings}, Amer. Math. Soc. Coll. Publ., vol. XXXVII, Amer. Math. Soc., Providence, R.I., 1956. \bibitem{jant} A.~Jantzen, \emph{Lectures on quantum groups}, Amer. Math. Soc., Providence, R.I., 1996. \bibitem{jimbo} M.~Jimbo, \emph{A $q$-difference analogue of ${U}({\bf g})$ and the {Y}ang--{B}axter equation}, Lett. Math. Phys. \textbf{10} (1985), no.~1, 63--69. \bibitem{jones89} V.~Jones and V.~S. Sunder, \emph{Introduction to subfactors}, London Math. Soc. Lect. Note. Ser., vol. 234, Cambridge Univ. Press, Cambridge, 1994. \bibitem{110} C.~Jordan, \emph{Essai sur la geometrie \`a $n$ dimensions}, Bull. Soc. Math. France \textbf{3} (1875), 103--174. \bibitem{jorg_book} P.~E.~T. J\o{}rgensen, \emph{Operators and representation theory}, North-Holland (Elsevier), Amsterdam, 1988. \bibitem{jor_moore} P.~E.~T. J\o{}rgensen and R.~T. Moore, \emph{Operator commutation relations}, D. Reidel Publ. Comp., Dordrecht, 1984. \bibitem{jorg_s_w} P.~E.~T. J\o{}rgensen, L.~M. Schmitt, and R.~F. Werner, \emph{{$q$}-{C}anonical commutation relations and stability of the {C}untz algebra}, Pacific J. Math. \textbf{165} (1994), 131--151. \bibitem{jorg} \bysame, \emph{Positive representation of general commutation relations allowing {W}ick ordering}, J. Funct. Anal. \textbf{134} (1995), 33--99. \bibitem{jorg_wer} P.~E.~T. J\o{}rgensen and R.~F. Werner, \emph{Coherent states of the $q$-canonical commutation relations}, Commun. Math. Phys. \textbf{164} (1994), 455--471. \bibitem{kac} V.~Kac, \emph{Root systems, representations of graphs and invariant theory}, Lect. Notes Math., vol. 996, pp.~74--108, Springer, Berlin, 1983. \bibitem{kad_rin} R.~V. Kadison and J.~R. Ringrose, \emph{Fundamentals of the theory of operator algebras, {I}, {II}}, Acad. Press, 1983, 1986. \bibitem{kal_sam} S.~A. Kalutsky and Yu.~S. Samo\u\i{}lenko, \emph{Periodic groups are not wild}, Ukr. Mat. Zh. \textbf{49} (1997), no.~5, 729--730, (Russian). \bibitem{kaz} D.~Kazhdan, \emph{Connection of the dual space of a group with the structure of its closed subgroups}, Funct. Anal. Appl. \textbf{1} (1957), 63--65. \bibitem{118} A.~Ya. Khelemski\u\i{}, \emph{Banach algebras and poly-normed algebras: general theory, representations, homologies}, Nauka, Moscow, 1989, (Russian). \bibitem{kiril2} A.~A. Kirillov, \emph{Dynamical systems, factors and representations of groups}, Uspekhi Mat. Nauk \textbf{22} (1967), no.~5, 67--80, (Russian). \bibitem{kiril} \bysame, \emph{Elements of the theory of representations}, Springer, Berlin, 1970. \bibitem{kis_sh} E.~Kissin and V.~Shul'man, \emph{Representations on {K}rein spaces and derivations of {$C^*$}-algebras}, Pitman Monographs and Surv. Pure Applied Math., vol.~89, Addison Wesley, Longman, 1997. \bibitem{kleinecke} D.~Kleinecke, \emph{On operator commutators}, Proc. Amer. Math. Soc. \textbf{8} (1957), 535--536. \bibitem{klles} S.~Klimek and A.~Lesniewski, \emph{Quantum {R}iemann surfaces. {I}. {T}he unit disc}, Commun. Math. Phys. \textbf{146} (1992), 103--122. \bibitem{klles2} S.~Klimek and A.~Lesniewski, \emph{A two-parameter quantum deformation of the unit disc}, Journ. Funct. Anal. \textbf{115} (1993), no.~1, 1--23. \bibitem{klim_sch} A.~U. Klimyk and K.~Schm\"udgen, \emph{Quantum groups and their representations}, Texts and Monographs in Physics, Springer, Berlin, Heidelberg, 1997. \bibitem{koe} H.~T. Koelink, \emph{On $*$-representations of the {H}opf $*$-algebra associated with the quantum group {$U_q(N)$}}, Compositio Math. \textbf{77} (1991), 199--231. \bibitem{koor_sw} T.~H. Koornwinder and R.~F. Swarttouw, \emph{On $q$-analogues of the {F}ourier and {H}ankel transforms}, Trans. Amer. Math. Soc. \textbf{333} (1992), 445--461. \bibitem{kor_soi} L.~I. Korogodski and Y.~S. Soibelman, \emph{Algebras of functions on quantum groups. {P}art 1}, Amer. Math. Soc., Providence, R.I., 1998. \bibitem{krugl_q} S.~A. Kruglyak, \emph{Representations of free involutive quivers}, Representations and quadratic forms, Inst. Math. Acad. Sci. Ukr. SSR, Kiev, 1979, pp.~149--151, (Russian). \bibitem{84} S.~A. Kruglyak, \emph{Representations of involutive quivers}, VINITI 7266-84, 1984, (Russian). \bibitem{85} S.~A. Kruglyak and A.~Yu. Piryatinskaya, \emph{On ``wild'' $*$-algebras and the unitary classification of weakly centered operators}, Prepr. ser. of Mittag-Leffler Inst. no.~11, 1995/96. \bibitem{krusam} S.~A. Kruglyak and Yu.~S. Samo\u\i{}lenko, \emph{On unitary equivalence of collections of self-adjoint operators}, Funct. Anal. i Prilozhen. \textbf{14} (1980), no.~1, 60--62, (Russian). \bibitem{kru_sam98} \bysame, \emph{Structure theorems for families of idempotents}, Ukr. Mat. Zhurn. \textbf{50} (1998), no.~4, 523--533, (Russian). \bibitem{kru_sam_ams} \bysame, \emph{On complexity of description of representations of $*$-algebras generated by idempotents}, Proc. Amer. Math. Soc. \textbf{128} (2000). \bibitem{142} N.~Krupnik, \emph{Banach algebras with symbol and singular integral operators}, Oper. Theory Adv. Appl., vol.~90, Birkh{\"a}user Verlag, Basel, 1987. \bibitem{kru_r_s} N.~Krupnik, S.~Roch, and B.~Silbermann, \emph{On {$C^*$}-algebras generated by idempotents}, J. Func. Anal. \textbf{137} (1996), 303--319. \bibitem{125} N.~Krupnik and E.~Spigel, \emph{Invertibility symbols for a {B}anach algebra generated by two idempotents and a shift}, Int. Equat. Oper. Theory \textbf{17} (1993), 597--578. \bibitem{kru_wor} P.~Kruszy\'nski and S.~L. Woronowicz, \emph{A noncommutative {G}elfand--{N}aimark theorem}, J. Oper. Theory \textbf{8} (1982), 361--389. \bibitem{kul} P.~P. Kulish, \emph{Contraction of quantum algebras and $q$-oscillators}, Teor. Math. Phys. \textbf{86} (1991), 108--110. \bibitem{kul_re} P.~P. Kulish and N.~Yu. Reshtikhin, \emph{Quantum linear problem for the sine-{G}ordon equation and higher representations}, Zap. Nauch. Sem. LOMI \textbf{101} (1981), 101--110, (Russian). \bibitem{lac} M.~Laca, \emph{Endomorphisms of {$\mathcal B(\mathcal H)$} and {C}untz algebras}, J. Oper. Theory \textbf{30} (1993), 85--101. \bibitem{lance95} E.~C. Lance, \emph{Hilbert {$C^*$}-modules: a toolkit for operator algebraists}, London Math. Soc. Lect. Notes Ser., vol. 210, CUP, 1995. \bibitem{10} E.~C. Lance, \emph{Finitely presented {$C^*$}-algebras}, Operator Algebras and Applications (A.~Katavolos, ed.), Nato ASI Series, Ser. C: Math. and Phys. Sci., vol. 495, Kluwer Acad. Publ., 1997, pp.~255--266. \bibitem{17} T.~A. Loring, \emph{{$C^*$}-algebras generated by stable relations}, J. Funct. Anal. \textbf{112} (1993), no.~1, 159--203. \bibitem{lus} G.~Lusztig, \emph{Introduction to quantum groups}, Birkh\"auser, Boston, 1993. \bibitem{macf} A.~J. Macfarlane, \emph{On $q$-analogues of the quantum harmonic oscillator and the quantum group $su(2)$}, J. Phys. A \textbf{22} (1989), 4581--4586. \bibitem{mackey1} G.~W. Mackey, \emph{Imprimitivity for representations of locally compact groups}, Proc. Nat. Acad. Sci. USA \textbf{35} (1949), no.~9, 537--545. \bibitem{mackey} \bysame, \emph{Induced representations of locally compact groups}, Ann. Math. \textbf{55} (1952), no.~1, 101--139. \bibitem{mad1} S.~Madjid, \emph{Foundations of quantum group theory}, Cambridge Univ. Press, Cambridge, 1995. \bibitem{manin2} Yu.~I. Manin, \emph{Topics in non-commutative geometry}, Princeton Univ. Press, Princeton, N.J., 1991. \bibitem{masuda_etal} T~Masuda, K.~Mimachi, Y.~Makagami, M.~Noumi, Y.~Saburi, and K.~Ueno, \emph{Unitary representations of the quantum group {$SU_q(1,1)$}}, Lett. Math. Phys. \textbf{19} (1990), no.~3, 187--204. \bibitem{20} K.~McClanahan, \emph{{$C^*$}-algebras generated by elements of a unitary matrix}, J. Funct. Anal. \textbf{107} (1992), no.~2, 439--457. \bibitem{rodm2} S.~A. McCullough and L.~Rodman, \emph{Two self-adjoint operators in {K}rein spaces}, Int. Equat. Oper. Theory \textbf{26} (1996), 202--209. \bibitem{men_shar} R.~Menikoff and D.~H. Sharp, \emph{Representations of a local current algebra: their dynamical determination}, J. Math. Phys. \textbf{16} (1975), no.~12, 2341--2360. \bibitem{mis} M.~Misiurewicz, \emph{Absolutely coninuous measures for certain maps of an interval}, Publ. Math. Inst. Hautes Etud. Sci. \textbf{53} (1981), 17--51. \bibitem{mormu} B.~Morrel and P.~Muhly, \emph{Centered operators}, Studia Math. \textbf{51} (1974), 251--263. \bibitem{murphy} G.~J. Murphy, \emph{{$C^*$}-algebras and operator theory}, Acad. Press, Boston, 1990. \bibitem{murneu} F.~Murray and J.~von Neumann, \emph{On rings of operators.{ IV.}}, Ann. Math. \textbf{44} (1943), 71--808. \bibitem{nagy_nica2} G.~Nagy and A.~Nica, \emph{On the ``quantum disk'' and ``non-commutative circle''}, Algebraic methods in operator theory (R.~E. Curto and P.~E.~T. J\o{}rgensen, eds.), Birkh\'auser Velag, Boston, 1994, pp.~276--290. \bibitem{naz} L.~A. Nazarova, \emph{Representations of a quadruple}, Izv. AN. SSSR \textbf{31} (1967), no.~6, 1361--1377, (Russian). \bibitem{nelson} E.~Nelson, \emph{Analytic vectors}, Ann. of Math. \textbf{70} (1959), no.~2, 572--615. \bibitem{newt} I.~Newton, \emph{Enumeratio linearum portii ordinis}, Optics (1704), 138--162. \bibitem{niz_tur} L.~P. Nizhnik and L.~B. Turowska, \emph{Representations of double commutator by matrix-differential operators}, Methods Funct. Anal. Topol. \textbf{3} (1997), no.~3, 75--80. \bibitem{noumi} M.~Noumi and K.~Mimachi, \emph{Big $q$-{J}acobi polynomials, $q$-{H}ahn polynomials and a family of quantum $3$-spheres}, Lett. Math. Phys. \textbf{19} (1990), no.~4, 299--305. \bibitem{odes} A.~V. Odesski, \emph{On an analogue of the {S}klyanin algebra}, Funct. Anal. Appl. \textbf{20} (1986), 152--154. \bibitem{odes_fei} A.~V. Odesski and B.~L. Feigin, \emph{Elliptic {S}klyanin algebras}, Funkt. Anal. Prilozh. \textbf{23} (1989), no.~3, 45--54. \bibitem{ols_zame} C.~L. Olsen and W.~R. Zame, \emph{Singly generated {$C^*$}-algebras}, Trans. Amer. Math. Soc. \textbf{215} (1976), 205--215. \bibitem{olsh} A.~Yu. Ol'shanski\u\i, \emph{Geometry of defining relations in groups}, Kluwer Acad. Publ., Dordrecht, 1991, Transl from Russian edn.: Nauka, Moscow, 1989. \bibitem{three} V.~L. Ostrovsky\u\i{}, \emph{Representations of a family of quadratic algebras with three generators}, Selecta Math. Sov. \textbf{12} (1993), 119--127. \bibitem{vo_mfat} \bysame, \emph{On operator relations, centered operators, and nonbijective dynamical systems}, Methods Funct. Anal. Topol. \textbf{2} (1996), no.~3-4, 114--121. \bibitem{umz88} V.~L. Ostrovsky\u\i{} and Yu.~S. Samo\u\i{}lenko, \emph{Application of the projection spectral theorem to noncommuting families of operators}, Ukr. Math. Zh. \textbf{40} (1988), no.~4, 469--481, (Russian). \bibitem{fa} \bysame, \emph{Families of unbounded selfadjoint operators, which are connected with non-{L}ie relations}, Funct. Anal. Prilozh. \textbf{23} (1989), no.~2, 67--68, (Russian). \bibitem{lomi} \bysame, \emph{Representations of $*$-algebras with two generators and polynomial relations}, Zap. Nauchn. Semin. LOMI \textbf{172} (1989), no.~%, 121--129, (Russian). \bibitem{romp} \bysame, \emph{Unbounded operators satisfying non-{L}ie commutation relations}, Repts. math. phys. \textbf{28} (1989), no.~1, 91--103. \bibitem{adv} \bysame, \emph{Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation}, Adv. Sov. Math. \textbf{9} (1992), 131--149. \bibitem{slie} \bysame, \emph{On pairs of self-adjoint operators}, Seminar Sophus Lie \textbf{3} (1993), no.~2, 185--218. \bibitem{umz95} \bysame, \emph{On representations of the {H}eisenberg relations for the quantum {$E(2)$} group}, Ukr. Mat. Zh. \textbf{47} (1995), no.~5, 689--692. \bibitem{non} \bysame, \emph{Representations of $*$-algebras and dynamical systems}, Nonlinear Math. Phys. \textbf{2} (1995), no.~2, 133--150. \bibitem{romp2} \bysame, \emph{Representations of quadratic $*$-algebras by bounded and unbounded operators}, Repts. Math. Phys. \textbf{35} (1995), no.~2/3, 283--301. \bibitem{ossilv} V.~L. Ostrovsky\u\i{} and S.~D. Silvestrov, \emph{Representations of the real forms of a graded analogue of the {L}ie algebra {$sl(2,\Bbb C)$}}, Ukr. Mat. Zhurn. \textbf{44} (1992), no.~11, 1518--1524, (Russian). \bibitem{ostur} V.~L. Ostrovsky\u\i{} and L.~B. Turovskaya, \emph{Representations of $*$-algebras and multidimensional dynamical systems}, Ukr. Mat. Zhurn. \textbf{47} (1995), no.~4, 488--497. \bibitem{partas} K.~R. Parthasarathy, \emph{An introduction to quantum stochastic calculus}, Birkh"auser--Verlag, Basel, 1992. \bibitem{pear} C.~Pearcy, \emph{On certain von~{N}eumann algebras which are generated by partial isometries}, Proc. Amer. Math. Soc. \textbf{15} (1964), 393--395. \bibitem{ped2} G.~K. Pedersen, \emph{Measure theory for {$C^*$}-algebras}, Math. Scand. \textbf{22} (1968), 63--74. \bibitem{28} \bysame, \emph{{$C^*$}-algebras and their automorphism groups}, London Math. Soc. Monographs, vol.~14, Acad. Press, London, 1979. \bibitem{ped} S.~Pedersen, \emph{Anticommuting selfadjoint operators}, J. Funct. Anal. \textbf{89} (1990), no.~2, 428--443. \bibitem{15} N.~C. Phillips, \emph{Inverse limits of {$C^*$}-algebras}, J. Oper. Theory \textbf{19} (1988), 153--195. \bibitem{33} R.~S. Pierce, \emph{Associative algebras}, Graduate texts in math., vol.~88, Springer-Verlag, New York--Heidelberg--Berlin, 1982. \bibitem{piryat} A.~Piryatinskaya, \emph{On unitary classification of weakly centered operators}, Vestnik Tambov Univ. \textbf{3} (1998), no.~1, 79--83. \bibitem{pirsam} A.~Yu. Piryatinskaya and Yu.~S. Samo\u\i{}lenko, \emph{Wild problems in representation theory of $*$-algebras with generators and relations}, Ukr. Mat. Zhurn. \textbf{47} (1995), no.~1, 70--78, (Russian). \bibitem{pop_snmp} S.~Popovych, \emph{Representations of real forms of {W}itten's first deformation}, Symmetry Nonlin. Math. Phys. \textbf{2} (1997), 393--396. \bibitem{pop_mfat} \bysame, \emph{Unbounded idempotents}, Methods Funct. Anal. Topol. \textbf{5} (1999), no.~1. \bibitem{pow_i} R.~T. Powers, \emph{Selfadjoint algebras of unbounded operators. {I}}, Commun. Math. Phys. \textbf{21} (1971), 85--124. \bibitem{pow} \bysame, \emph{Selfadjoint algebras of unbounded operators. {II}}, Trans Amer. Math. Soc. \textbf{187} (1974), 261--293. \bibitem{30} \bysame, \emph{Simplicity of the {$C^*$}-algebra associated with the free group on two generators}, Duke Math. J. \textbf{42} (1975), 151--156. \bibitem{proskurin} D.~Proskurin, \emph{Homogeneous ideals in {W}ick algebras}, Proc. Amer. Math. Soc. \textbf{126} (1998), no.~11, 3371--3376. \bibitem{pro_mfat} D.~P. Proskurin, \emph{About positivity of {F}ock inner product of a certain {W}ick algebras}, Methods Funct. Anal. Topol. \textbf{5} (1999), no.~1. \bibitem{pro} D.~P. Proskurin and Yu.~S. Samo\u\i{}lenko, \emph{Representations of {W}ick {CCR} algebra}, Spectral and evolutionary problems, vol. 8 (Simferopol), Tavria, 1998, pp.~43--45. \bibitem{pusz_anti} W.~Pusz, \emph{Twisted canonical anticommutation relations}, Repts. Math. Phys. \textbf{27} (1989), 349--360. \bibitem{pw} W.~Pusz and S.~L. Woronowicz, \emph{Twisted second quantization}, Repts. Math. Phys. \textbf{27} (1989), 231--257. \bibitem{36} I.~F. Putnam, \emph{{$C^*$}-algebras arising from interval exchange transformations}, J. Oper. Theory \textbf{27} (1992), 231--250. \bibitem{rab_mfat} V.~I. Rabanovich, \emph{Banach algebras generated by three idempotents}, Methods Funct. Anal. Topol. \textbf{4} (1998), no.~1, 65--67. \bibitem{rab_umz} \bysame, \emph{Singly generated {$C^*$}-algebras}, Ukr. Mat. Zh. \textbf{51} (1999), no.~8, (Russian). \bibitem{rab_sam_mfat} V.~I. Rabanovich and Yu.~S. Samo\u\i{}lenko, \emph{On representations of {$\mathcal{F}_n$}-algebras and invertibility symbols}, Methods Funct. Anal. Topol. \textbf{4} (1998), no.~4, 86--96. \bibitem{rab_sam_ieot} \bysame, \emph{On representations of {$F_n$}-algebras and their applications}, Oper. Theory Adv. Appl., vol.~94, Birkh\"auser Verlag, Basel, 1999. \bibitem{rab_sam_fa} \bysame, \emph{When a sum of idempotents or orthoprojections is multiple of the identity}, Funct. Anal. Prilozh. \textbf{39} (2000). \bibitem{115} I.~Raeburn and A.~M. Sinclair, \emph{The {$C^*$}-algebra generated by two projections}, Math. Scand. \textbf{65} (1989), 278--290. \bibitem{reedsim} M.~Reed and B.~Simon, \emph{Methods of modern mathematical physics}, vol.~1, Acad. Press, New York, 1972. \bibitem{renau} J.~Renault, \emph{A groupoid approach to {$C^*$}-algebras}, Lect. Notes. Math., vol. 793, Springer--Verlag, 1980. \bibitem{rief_book} M.~Rieffel, \emph{Quantum deformations for actions of {$\mathbb{R}^d$}}, Mem. Amer. Math. Soc., vol. 506, Amer. Math. Soc., Providence, RI, 1993. \bibitem{rief74} M.~A. Rieffel, \emph{Morita equivalence for {$C^*$}-algebras and {$W^*$}-algebras}, J. Pure Appl. Algebra \textbf{5} (1974), 51--96. \bibitem{124} S.~Roch and B.~Sibermann, \emph{Algebras generated by idempotents and the symbol calculus for singular integral operators}, Int. Equat. Oper. Theory \textbf{11} (1988), 385--419. \bibitem{roi_box} A.~V. Roiter, \emph{Boxes with an involution}, Representations and quadratic forms, Inst. Math. Acad. Sci. Ukr. SSR, Kiev, 1979, pp.~124--126, (Russian). \bibitem{137} W.~Rudin, \emph{Functional analysis}, McGraw-Hill, New York, 1973. \bibitem{sak} S.~Sakai, \emph{Operator algebras in dynamical systems. {T}he theory of unbounded derivations in {$C^*$}-algebras}, Cambridge Univ. Press, Cambrige, 1991. \bibitem{book} Yu.~S. Samo\u\i{}lenko, \emph{Spectral theory of families of self-adjoint operators}, Kluwer Academic Publisher, 1991, Transl. from Russian edn.: Naukova Dumka, Kiev, 1984. \bibitem{sam_sh_umz} Yu.~S. Samo\u\i{}lenko and V.~S. Shul'man, \emph{On representations of relations of the form {$i[A,B]=f(A) + g(B)$}}, Ukr. Mat. Zh. \textbf{43} (1991), no.~1, 110--114, (Russian). \bibitem{sam_tur} Yu.~S. Samo\u\i{}lenko and L.~B. Turowska, \emph{On representations of $*$-algebras by unbounded operators}, Funkt. Anal. Prilozh. \textbf{31} (1997), no.~4, 80--83, (Russian). \bibitem{100} \bysame, \emph{Representations of cubic semilinear relations and real forms of the {F}airlie algebra}, Quantum groups and quantum spaces, Banach Center Publ., vol.~40, Inst. Math. Polish Acad. Sci., Warszawa, 1997, pp.~21--40. \bibitem{119} Yu.~S. Samo\u\i{}lenko, L.~B. Turowska, and S.~Popovych, \emph{Representations of a cubic deformation of {$su(2)$} and parasupersymmetric commutation relations}, Symmetry in Nonlin. Math. Phys. \textbf{2} (1997), 272--383. \bibitem{sam_tur_sh} Yu.~S. Samo\u\i{}lenko, L.~B. Turowska, and V.~S. Shul'man, \emph{Semilinear relations and their $*$-representations}, Methods Funct. Anal. Topol. \textbf{2} (1996), no.~1, 55--111. \bibitem{135} K.~Schm{\"u}dgen, \emph{Unbounded operator algebras and representation theory}, Birkh\"auser, Basel, 1990. \bibitem{133} \bysame, \emph{Operator representations of {$\mathbb{R}_q$}}, Publ RIMS \textbf{28} (1992), no.~6, 1029--1061. \bibitem{132} \bysame, \emph{Integrable operator representations of {$\mathbb{R}_q^2$}, {$X_{q,\gamma}$} and {$SL(2,\mathbb{R})$}}, Commun. Math. Phys \textbf{159} (1994), 217--237. \bibitem{134} \bysame, \emph{Operator representations of {$U_q(sl_2(\mathbb{R}))$}}, Lett. Math. Phys. \textbf{37} (1996), 211--222. \bibitem{shwe_we} J.~Schwenk and J.~Wess, \emph{A {$q$}-deformed quantum mechanical toy model}, Phys. Lett. B. \textbf{291} (1992), 273--277. \bibitem{serg84} V.~V. Sergeichuk, \emph{Classification of linear operators in a finite-dimensional unitary space}, Funct. Anal. Appl. \textbf{18} (1984), no.~3, 224--230. \bibitem{serg87} \bysame, \emph{Classification problems for systems of forms and linear mappings}, Math. USSR Izvestiya \textbf{31} (1988), no.~3, 481--501. \bibitem{serg90} \bysame, \emph{Classification of pairs of subspaces in spaces with scalar product}, Ukrain. Math. J. \textbf{42} (1990), no.~4, 478--491. \bibitem{serg92} \bysame, \emph{Symmetric representations of algebras with involution}, Math. Notes \textbf{50} (1992), no.~3--4, 1058--1061. \bibitem{86} \bysame, \emph{Unitary and {E}uclidean representations of a quiver}, Linear Algebra Appl. \textbf{278} (1998), 37--62. \bibitem{shapiro} H.~Shapiro, \emph{A survey of canonical forms and invariants for unitary similarity}, Linear Algebra Appl. \textbf{147} (1991), 101--167. \bibitem{shmr} A.~N. Sharkovski\u\i{}, Yu.~L. Maistrenko, and E.~Yu. Romanenko, \emph{Difference equations and their applications}, Kluwer Acad. Publ., Dordrecht, 1993, Transl. from Russian edn.: Naukova Dumka, Kiev, 1986. \bibitem{sh_kol_etal} A.~N. Sharkovsky, S.~F. Kolyada, A.~G. Sivak, and V.~V. Fedorenko, \emph{Dynamics of one-dimensional maps}, Kluwer Acad. Publ., Dordrecht, 1997, Transl. from Russian edn.: Naukova Dumka, Kiev, 1989. \bibitem{shirokov} F.~V. Shirokov, \emph{Proof of the {K}aplansky hypothesis}, Uspekhi Mat. Nauk \textbf{11} (1956), 167--168, (Russian). \bibitem{143} V.~S. Shulman, \emph{Multiplication operators and spectral synthesis}, Dokl. Akad. Nauk SSSR \textbf{313} (1990), no.~5, 1047--1051, (Russian). \bibitem{82} S.~D. Silvestrov, \emph{Hilbert space representations of the graded analogue of the {L}ie algebra of the group of plane motions}, Studia Math. \textbf{117} (1996), no.~2, 195--203. \bibitem{81} \bysame, \emph{Representations of commutation relations. {A} dynamical systems approach}, Hadronic Journ. Suppl. \textbf{11} (1996), no.~1, 1--116. \bibitem{silv} S.~D. Silvestrov and L.~B. Turowska, \emph{Representations of the $q$-deformed {L}ie algebra of the group of motions of the {E}uclidean plane}, J. Funct. Anal. \textbf{160} (1998), 79--114. \bibitem{83} S.~D. Silvestrov and H.~Wallin, \emph{Representations of algebras associated with {M}{\"o}bius transformation}, J. Nonlin. Math. Phys. \textbf{3} (1996), no.~1-2, 202--213. \bibitem{sin} Ya.~G. Sinai, \emph{Modern problems of egodic theory}, Modern Problems of Mathematics, Fiziko-Matematicheskaya Literatura, Moscow, 1995. \bibitem{sklyan} E.~K. Sklyanin, \emph{On some algebraic structures related to {Y}ang--{B}axter equation}, Funkt. Anal. i Prilozhen. \textbf{16} (1982), no.~4, 27--34, (Russian). \bibitem{skl_2} \bysame, \emph{On some algebraic structures related to the {Y}ang--{B}axter equation. {II}. {R}epresentations of quantum algebra}, Funct. Anal. Prilozh. \textbf{17} (1983), no.~4, 34--48, (Russian). \bibitem{smst} A.~S. Smogorzhevski\u\i{} and E.~S. Stolova, \emph{Handbook in the theory of plane curves of the third order}, Fizmatgiz, Moscow, 1961, (Russian). \bibitem{138} Ya.~S. Soibelman and L.~L. Vaksman, \emph{The algebra of functions on the quantum group {$SU(n+1)$} and odd-dimensional quantum spheres}, Algebra i Analiz \textbf{2} (1990), no.~5, 101--120, (Russian). \bibitem{str_voi} S.~Stratila and D.~Voiculescu, \emph{Representations of {AF}-algebras and of the group {$U(\infty)$}}, Lect. Notes. Math., vol. 486, Springer, 1975. \bibitem{take79} M.~Takesaki, \emph{Theory of operator algebras}, Springer, 1979. \bibitem{tam} P.~K. Tam, \emph{On the unitary equivalence of certain classes of non-normal operators. {I}}, Canad. J. Math. \textbf{23} (1971), no.~5, 849--856. \bibitem{11} P.~Tapper, \emph{Embedding $*$-algebras into {$C^*$}-algebras}, Ph. d. thesis, Univ. of Leeds, 1996. \bibitem{thoma} E.~Thoma, \emph{{\"U}ber unit\"are {D}arstellungen abz\"ahlbarer, diskretten {G}ruppen}, Math. Ann. \textbf{153} (1964), 111--138. \bibitem{tomi} J.~Tomijama, \emph{Invitation to the ${C}^*$-algebtas and topological dynamics}, World Sci. Publ., Singapore, 1987. \bibitem{26} D.~M. Topping, \emph{Lectures on von {N}eumann algebras}, Van Nostrand Reinhold Comp., London, 1971. \bibitem{144} L.~Turovskaya, \emph{Representations of some real forms of {$U_q(sl(3))$}}, Algebras, Groups and Geometries \textbf{12} (1995), 321--338. \bibitem{130} E.~Twietmeyer, \emph{Real forms of {$U_q(\mathfrak{J})$}}, Lett. Math. Phys. \textbf{24} (1992), no.~1, 49--59. \bibitem{vakskor} L.~L. Vaksman and L.~I. Korogodskii, \emph{The algebra of bounded functions on the quantum group of motions of the plane and $q$-analog of {B}essel functions}, Dokl. Akad. Nauk USSR \textbf{304} (1989), no.~5, 1036--1040, (Russian). \bibitem{vas} F.-H. Vasilescu, \emph{Anticommuting selfadjoint operators}, Rev. Roum. Math. Pures Appl. \textbf{28} (1983), 77--91. \bibitem{vasi} A.~N. Vasil'ev, \emph{Theory of representations of a topological (non-{B}anach) involutary algebra}, Teor. Math. Phys. \textbf{2} (1970), 113--123. \bibitem{vasil} N.~Vasilevski, \emph{{$C^*$}-algebras generated by projections and their applications}, Integr. Equat. Oper. Theory \textbf{31} (1998), 113--132. \bibitem{114} N.~Vasilevski and I.~Spitkovski, \emph{On algebra generated by two projections}, Dokl. Akad. Nauk Ukr. SSR, Ser. A \textbf{8} (1981), 10--13, (Russian). \bibitem{vai3} E.~Ye. Vaysleb, \emph{Infinite-dimensional $*$-representations of {S}klyanin algebra in degenerate case (the quantum algebra {$U_q(sl(2))$})}, Methods of Functional Analysis in problems of Mathematical Physics, Inst. Math. Acad. Sci. Ukr. SSR, Kiev, 1990, pp.~50--62, (Russian). \bibitem{vai} \bysame, \emph{Representations of relations which connect a family of commuting operators with non-sefadjoint one}, Ukrain. Math. Zh. \textbf{42} (1990), 1258--1262, (Russian). \bibitem{vai_fed} E.~Ye. Vaysleb and V.~V. Fedorenko, \emph{Representations of operator relations and one-dimensional dynamical systems}, Application of Methods of Functional Analysis in Mathematical Physics, Inst. Math. Akad. Nauk UkrSSR, Kiev, 1989, (Russian), pp.~12--20. \bibitem{vaisam1} E.~Ye. Vaysleb and Yu.~S. Samo\u\i{}lenko, \emph{Representations of operator relations by unbounded operators and multi-dimensional dynamical systems}, Ukrain. Math. Zh. \textbf{42} (1990), no.~9, 1011--1019, (Russian). \bibitem{vai_sam_sel} \bysame, \emph{Representations of the relations {$AU = UF(A)$} by unbounded self-adjoint and unitary operators}, Selecta Math. Sov. \textbf{13} (1994), no.~1, 35--54. \bibitem{ver} A.~M. Vershik, \emph{Algebras with quadratic relations}, Spectral theory of operators and infinite-dimensional analysis, Inst. Math Acad. Sci. Ukraine, Kiev, 1984, (Russian), pp.~32 -- 56. \bibitem{ver_gel_g2} A.~M. Vershik, I.~M. Gelfand, and M.~I. Graev, \emph{Representations of the group {$SL(2,R)$}, where {$R$} is a function ring}, Uspehi Mat. Nauk \textbf{28} (1973), no.~5, 83--128, (Russian). \bibitem{ver_gel_g} \bysame, \emph{Commutative model of the representation of the current group {$SL(2, \mathbb{R})^X$} related to the unipotent subgroup}, Funct. Anal. Priolozh. \textbf{17} (1983), no.~2, 70--72, (Russian). \bibitem{voi_dy_ni} D.~V. Voiculescu, K.~J. Dykema, and A.~Nica, \emph{Free random variables}, CRM Monograph Ser., Centre de Recherches Math. Univ. Motr\'eal, vol.~1, Amer. Math. Soc., Providence, R. I., 1992. \bibitem{yzette} Y.~Weiss, \emph{On algebras generated by two idempotents}, Seminar Analysis: Operator Equations and Numer. Anal. 1987/88 (Berlin), Karl-Weierstrass-Institut f\"ur Mathematik, 1988, pp.~139--145. \bibitem{wen} H.~Wenzl, \emph{Representations of braid groups and the quantum {Y}ang--{B}axter equation}, Pacif. J. Math. \textbf{145} (1990), 153--180. \bibitem{wich} J.~Wichmann, \emph{Hermitian $*$-algebras which are not symmetric}, J. London Math. Soc. \textbf{8} (1974), 109--112. \bibitem{wielandt} H.~Wielandt, \emph{{\"U}ber die {U}nbeschr\'anktheit der {O}peratoren des {Q}uantenmechanik}, Math. Ann. \textbf{121} (1949), 21. \bibitem{103} E.~Witten, \emph{Gauge theories, vertex models, and quantum groups}, Repts. Nuclear Phys. \textbf{b330} (1990), 285--346. \bibitem{wog_2} W.~R. Wogen, \emph{On generators for von~{N}eumann algebras}, Bull. Amer. Math. Soc. \textbf{75} (1969), 95--99. \bibitem{wog} \bysame, \emph{On special generators for properly infinite von~{N}eumann algebras}, Proc. Amer. Math. Soc. \textbf{28} (1971), no.~1, 107--113. \bibitem{wor87} S.~L. Woronowicz, \emph{Compact matrix pseudogroups}, Commun. Math. Phys. \textbf{111} (1987), 613--665. \bibitem{wor} \bysame, \emph{Quantum {$E(2)$} group and its {P}ontryagin dual}, Lett. Math. Phys. \textbf{23} (1991), 251--263. \bibitem{woraff} \bysame, \emph{Unbounded elements affiliated with ${C}^*$-algebras and non-compact quantum groups}, Commun. Math. Phys. \textbf{136} (1991), 399--432. \bibitem{wor_aff_2} \bysame, \emph{{$C^*$}-algebras generated by unbounded elements}, Rev. Math. Phys. \textbf{7} (1995), no.~3, 481--521. \bibitem{yama} Sh. Yamagami, \emph{On unitary representation theories of compact quantum groups}, Commun. Math. Phys. \textbf{167} (1995), 509--529. \bibitem{zachos} C.~Zachos, \emph{Elementary paradigms of quantum algebras}, Cont. Math. \textbf{134} (1992), 351--377. \bibitem{zak} S.~Zakrzewski, \emph{Realifications of complex quantum groups}, Groups and related topics (R.~I.~Gielerak et~al., ed.), Kluwer Acad. Publ., Dordrecht, 1992, pp.~83--100. \bibitem{zhe} A.~S. Zhedanov, \emph{{$Q$}-rotations and other {$Q$}-transformations as unitary nonlinear automorphisms of quantum algebras}, J. Math. Phys. \textbf{35} (1994), 3756--3764. \bibitem{zhel} D.~P. Zhelobenko, \emph{Compact {L}ie groups and their representations}, Translations of Math. Monographs., vol.~40, Amer. Math. Soc., Providence, R.I., 1973, Trans. from Russian edn.: Nauka, Moscow, 1970. \end{thebibliography}