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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} 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\indexentry{theorem!Kleinecke--Shirokov}{43} \indexentry{theorem!Jacobson}{44} \indexentry{relations!semilinear}{44} \indexentry{theorem!Kleinecke--Shirokov type}{44} \indexentry{relation!semilinear!characteristic function}{47} \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}{65} \indexentry{Jacobi matrix}{73} \indexentry{deficiency indices}{73} \indexentry{representation!Fock}{74} \indexentry{Wold decomposition}{75} \indexentry{real quantum plane}{75} \indexentry{real quantum hyperboloid}{75} \indexentry{theorem!Fuglede--Putnam--Rosenblum}{75} \indexentry{second-degree mapping}{83} \indexentry{continued 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identity!non-orthogonal}{110} \indexentry{projections!four-tuple}{110} \indexentry{Witten's deformations of $so(3)$}{119} \indexentry{Sklyanin algebra}{123} \indexentry{Fairlie algebra}{133} \indexentry{dynamical system!triangular}{155} \indexentry{twisted CCR}{155} \indexentry{twisted CAR}{155} \indexentry{CCR@$\mu$-CCR algebra}{155} \indexentry{CAR@$\mu$-CAR algebra}{158} \indexentry{quantum sphere}{166} \indexentry{Heisenberg relations}{169} \indexentry{Wick algebra}{173} \indexentry{Wick ordered monomials}{174} \indexentry{Wick ideal}{174} \indexentry{commutative model}{180} \indexentry{operator!centered}{185} \indexentry{Cuntz algebra}{189} \indexentry{measure!product}{194} \indexentry{majorization}{203} \indexentry{wildness@$*$-wildness}{203} \indexentry{majorization}{206} \indexentry{algebra@$*$-algebra!wild}{212} \indexentry{wildness@$*$-wildness}{212} \indexentry{standard $*$-wild problem}{213} \indexentry{algebra@$*$-algebra!$*$-wild}{214} \indexentry{projections!all but one orthogonal}{217} \indexentry{projections!four-tuples}{217} \indexentry{idempotents!pairwise orthogonal}{220} \indexentry{idempotents!commuting pairs}{220} \indexentry{relations!$*$-wild!semilinear}{221} \indexentry{relations!$*$-wild!quadratic and cubic}{222} \indexentry{group!$*$-wild}{227} \indexentry{group!Coxeter!not affine}{228} \indexentry{group!hyperbolic}{228} \indexentry{group!amenable}{229} \indexentry{group!periodic}{229} \indexentry{group!Burnside}{229} \indexentry{operator!non-self-adjoint}{230} \indexentry{operator!quasi-normal}{233} \indexentry{operator!weakly centered}{234} \indexentry{operator!partial isometry}{234} \indexentry{operator!algebraic}{236} \indexentry{operator!hyponormal}{236} \indexentry{isomertries!commuting pair}{237}