\begin{theindex} \item algebra \subitem $F_n$-algebra, 27 \subitem enveloping pro-$C^*$, 20 \subitem enveloping $*$-algebra, 15 \subitem enveloping $\sigma$-$C^*$, 17 \subitem enveloping $C^*$, 16 \subitem residually finite dimensional, 13 \item $*$-algebra \subitem $*$-bounded, 16 \subitem $*$-wild, 214 \subitem $C^*$-representatble, 11 \subitem $\sigma$-$C^*$-representatble, 20 \subitem finitely generated, 21 \subitem generated by idempotents, 29 \subitem group, 11 \subitem locally $C^*$, 20 \subitem wild, 212 \subitem with generators and relations, 16 \indexspace \item Cantor set, 106 \item $\mu$-CAR algebra, 158 \item $\mu$-CCR algebra, 155 \item commutative model, 180 \item continued fractions, 84, 95 \item Cuntz algebra, 189 \indexspace \item deficiency indices, 73 \item dynamical system, 89 \subitem cycle, 89 \subitem measurable section, 90 \subitem non-bijective, 91 \subitem orbit, 89 \subitem periodic point, 89 \subitem triangular, 155 \indexspace \item Fairlie algebra, 133 \indexspace \item graded $so(3)$, 106 \item group \subitem $*$-wild, 227 \subitem amenable, 229 \subitem Burnside, 229 \subitem Coxeter, 32 \subsubitem not affine, 228 \subitem hyperbolic, 228 \subitem periodic, 229 \subitem residually finite, 13 \indexspace \item Heisenberg relations, 169 \indexspace \item idempotents \subitem commuting pairs, 220 \subitem pairwise orthogonal, 220 \item involution \subitem completely proper, 12 \subitem proper, 12 \item isomertries \subitem commuting pair, 237 \indexspace \item Jacobi matrix, 73 \indexspace \item Lie algebras \subitem nonlinear transformations, 26 \indexspace \item majorization, 203, 206 \item marginally null subset, 61 \item measurable section, 65 \item measure \subitem ergodic, 62, 90 \subitem product, 194 \subitem quasi-invariant, 62, 89 \indexspace \item non-commutative curves \subitem circle, 39 \subitem hyperbola, 39 \subitem pair of intersecting lines, 39 \indexspace \item operator \subitem algebraic, 236 \subitem centered, 86, 185 \subsubitem partial isometry, 97 \subitem hyponormal, 236 \subitem intertwining, 8 \subitem non-self-adjoint, 230 \subitem partial isometry, 234 \subitem pseudo-integral, 59 \subitem quasi-normal, 233 \subitem supporting set, 49 \subitem weakly centered, 234 \item operators \subitem bounded self-adjoint pair, 22 \subitem irreducible family, 21 \indexspace \item polynomial \subitem standard, 27 \item projections \subitem all but one orthogonal, 217 \subitem four-tuple, 106, 110 \subitem four-tuples, 217 \indexspace \item quantum disk, 84, 102, 105 \item quantum sphere, 166 \indexspace \item real quantum hyperboloid, 75 \item real quantum plane, 75 \item relations \subitem $q$-relations, 26 \item relation \subitem semilinear \subsubitem characteristic binary relation, 47 \subsubitem characteristic function, 47 \subsubitem graph, 47 \item relations \subitem $*$-wild, 26 \subsubitem quadratic and cubic, 222 \subsubitem semilinear, 221 \subitem quadratic, 24 \subsubitem homogeneous, 24 \subitem representation, 21 \subitem semilinear, 44 \item relations \subitem $F_4$-relations, 26 \item representation, 7 \subitem $*$-complete, 62 \subitem anti-Fock, 100 \subitem Fock, 74, 100 \subitem indecomposable, 9 \subitem irreducible, 9 \item representations \subitem category $\srep\mathfrak{A}$, 8 \subitem equaivalent, 7 \subitem residual family, 11 \subitem unitarily equivalent, 8 \item resolution of the identity \subitem non-orthogonal, 110 \indexspace \item second-degree mapping, 83, 94, 100, 105, 106 \item Sklyanin algebra, 123 \item standard $*$-wild problem, 213 \indexspace \item theorem \subitem Amitsur--Levitski, 27 \subitem Fuglede--Putnam--Rosenblum, 75 \subitem Jacobson, 44 \subitem Kleinecke--Shirokov, 43 \subitem Kleinecke--Shirokov type, 44, 48 \subitem Sharkovsky, 93 \item twisted CAR, 155 \item twisted CCR, 155 \indexspace \item Wick algebra, 173 \item Wick ideal, 174 \item Wick ordered monomials, 174 \item $*$-wildness, 203, 212 \item Witten's deformations of $so(3)$, 119 \item Wold decomposition, 75 \end{theindex}

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