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\indexentry{representation}{7} \indexentry{representations!equaivalent}{7} \indexentry{representations!unitarily equivalent}{8} \indexentry{representations!category $\srep\mathfrak{A}$}{8} \indexentry{operator!intertwining}{8} \indexentry{representation!irreducible}{9} \indexentry{representation!indecomposable}{9} \indexentry{representations!residual family}{11} \indexentry{algebra@$*$-algebra!$C^*$-representatble}{11} \indexentry{algebra@$*$-algebra!group}{11} \indexentry{involution!completely proper}{12} \indexentry{involution!proper}{12} \indexentry{algebra!residually finite dimensional}{13} \indexentry{group!residually finite}{13} \indexentry{algebra!enveloping $*$-algebra}{15} \indexentry{algebra!enveloping $C^*$}{16} \indexentry{algebra@$*$-algebra!with generators and relations}{16} \indexentry{algebra@$*$-algebra!$*$-bounded}{16} \indexentry{algebra!enveloping $\sigma$-$C^*$}{17} \indexentry{algebra@$*$-algebra!locally $C^*$}{20} \indexentry{algebra@$*$-algebra!$\sigma$-$C^*$-representatble}{20} \indexentry{algebra!enveloping pro-$C^*$}{20} \indexentry{algebra@$*$-algebra!finitely generated}{21} \indexentry{relations!representation}{21} \indexentry{operators!irreducible family}{21} \indexentry{operators!bounded self-adjoint pair}{22} \indexentry{relations!quadratic}{24} \indexentry{relations!quadratic!homogeneous}{24} \indexentry{relations!$*$-wild}{26} \indexentry{relations@relations!$F_4$-relations}{26} \indexentry{Lie algebras!nonlinear transformations}{26} \indexentry{realtions@relations!$q$-relations}{26} \indexentry{polynomial!standard}{27} \indexentry{algebra!$F_n$-algebra}{27} \indexentry{theorem!Amitsur--Levitski}{27} \indexentry{algebra@$*$-algebra!generated by idempotents}{29} \indexentry{group!Coxeter}{32} \indexentry{non-commutative curves!circle}{39} \indexentry{non-commutative curves!pair of intersecting lines}{39} \indexentry{non-commutative curves!hyperbola}{39} \indexentry{theorem!Kleinecke--Shirokov}{43} \indexentry{theorem!Jacobson}{44} \indexentry{relations!semilinear}{44} \indexentry{theorem!Kleinecke--Shirokov type}{44} \indexentry{relation!semilinear!characteristic function}{46} \indexentry{relation!semilinear!characteristic binary relation}{47} \indexentry{relation!semilinear!graph}{47} \indexentry{theorem!Kleinecke--Shirokov type}{48} \indexentry{operator!supporting set}{49} \indexentry{operator!pseudo-integral}{59} \indexentry{marginally null subset}{61} \indexentry{measure!quasi-invariant}{62} \indexentry{measure!ergodic}{62} \indexentry{representation!$*$-complete}{62} \indexentry{measurable section}{64} \indexentry{Jacobi matrix}{73} \indexentry{deficiency indices}{73} \indexentry{representation!Fock}{74} \indexentry{Wold decomposition}{74} \indexentry{real quantum plane}{75} \indexentry{real quantum hyperboloid}{75} \indexentry{theorem!Fuglede--Putnam--Rosenblum}{75} \indexentry{second-degree mapping}{81} \indexentry{continued fractions}{82} \indexentry{quantum disk}{82} \indexentry{operator!centered}{84} \indexentry{dynamical system}{87} \indexentry{dynamical system!orbit}{87} \indexentry{dynamical system!periodic point}{87} \indexentry{dynamical system!cycle}{87} \indexentry{measure!quasi-invariant}{87} \indexentry{measure!ergodic}{88} \indexentry{dynamical system!measurable section}{88} \indexentry{dynamical system!non-bijective}{88} \indexentry{theorem!Sharkovsky}{91} \indexentry{second-degree mapping}{92} \indexentry{continued fractions}{93} \indexentry{operator!centered!partial isometry}{94} \indexentry{representation!Fock}{98} \indexentry{representation!anti-Fock}{98} \indexentry{second-degree mapping}{98} \indexentry{quantum disk}{100} \indexentry{second-degree mapping}{103} \indexentry{quantum disk}{103} \indexentry{second-degree mapping}{103} \indexentry{Cantor set}{103} \indexentry{graded $so(3)$}{104} \indexentry{projections!four-tuple}{104} \indexentry{resolution of the identity!non-orthogonal}{107} \indexentry{projections!four-tuple}{108} \indexentry{Witten's deformations of $so(3)$}{117} \indexentry{Sklyanin algebra}{120} \indexentry{Fairlie algebra}{130} \indexentry{dynamical system!triangular}{152} \indexentry{twisted CCR}{152} \indexentry{twisted CAR}{152} \indexentry{CCR@$\mu$-CCR algebra}{153} \indexentry{CAR@$\mu$-CAR algebra}{155} \indexentry{quantum sphere}{163} \indexentry{Heisenberg relations}{166} \indexentry{Wick algebra}{170} \indexentry{Wick ordered monomials}{171} \indexentry{Wick ideal}{171} \indexentry{commutative model}{177} \indexentry{operator!centered}{182} \indexentry{Cuntz algebra}{186} \indexentry{measure!product}{191} \indexentry{majorization}{201} \indexentry{wildness@$*$-wildness}{201} \indexentry{majorization}{204} \indexentry{algebra@$*$-algebra!wild}{210} \indexentry{wildness@$*$-wildness}{210} \indexentry{standard $*$-wild problem}{211} \indexentry{algebra@$*$-algebra!$*$-wild}{212} \indexentry{projections!all but one orthogonal}{215} \indexentry{projections!four-tuples}{215} \indexentry{idempotents!pairwise orthogonal}{218} \indexentry{idempotents!commuting pairs}{218} \indexentry{relations!$*$-wild!semilinear}{219} \indexentry{relations!$*$-wild!quadratic and cubic}{220} \indexentry{group!$*$-wild}{225} \indexentry{group!Coxeter!not affine}{226} \indexentry{group!hyperbolic}{226} \indexentry{group!amenable}{227} \indexentry{group!periodic}{227} \indexentry{group!Burnside}{227} \indexentry{operator!non-self-adjoint}{228} \indexentry{operator!quasi-normal}{231} \indexentry{operator!weakly centered}{232} \indexentry{operator!partial isometry}{232} \indexentry{operator!algebraic}{234} \indexentry{operator!hyponormal}{234} \indexentry{isomertries!commuting pair}{235}
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