Jones index theory by Hilbert C*-bimodules and K-theory

DOI10.1090/S0002-9947-00-02392-8zbMath0954.46034OpenAlexW1539907607MaRDI QIDQ4485699

Tsuyoshi Kajiwara, Yasuo Watatani

Publication date: 18 June 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02392-8

zbMATH Keywords

\(K\)-theorySchur's lemmaHilbert \(C^\ast\)-bimodulesFrobenius reciprocityJones indexrepresentations of \(G\)-\(C^*\)-algebras

Mathematics Subject Classification ID

(C^*)-modules (46L08) (K)-theory and operator algebras (including cyclic theory) (46L80) Subfactors and their classification (46L37)

Related Items (31)

CONTINUOUS CROSSED PRODUCT OF HILBERT C*-BIMODULES ⋮ The generalized Picard groups for finite dimensional $C^*$-Hopf algebra coactions on unital $C^*$-algebras ⋮ Actions of symbolic dynamical systems on C*-algebras ⋮ Jones index theory for Hilbert \(C^*\)-bimodules and its equivalence with conjugation theory ⋮ Q-system completion for \(C^\ast 2\)-categories ⋮ The strong Morita equivalence for coactions of a finite-dimensional C^*-Hopf algebra on unital C^*-algebras ⋮ THE STRONG MORITA EQUIVALENCE FOR INCLUSIONS OF -ALGEBRAS AND CONDITIONAL EXPECTATIONS FOR EQUIVALENCE BIMODULES ⋮ Relative Morita equivalence of Cuntz–Krieger algebras and flow equivalence of topological Markov shifts ⋮ Fundamental group of simple \(C^{*}\)-algebras with unique trace. II ⋮ Jones type \(\mathrm{C}^\ast\)-basic construction in non-equilibrium Hopf spin models ⋮ Anomalous symmetries of classifiable C*-algebras ⋮ Realization of rigid \(C^\ast \)-bicategories as bimodules over type \(\mathrm{II}_1\) von Neumann algebras ⋮ Standard \(\lambda\)-lattices, rigid \(\mathrm{C}^\ast\) tensor categories, and (bi)modules ⋮ Fourier-theoretic inequalities for inclusions of simple \(C^*\)-algebras ⋮ Amenability and vanishing of \(L^2\)-Betti numbers: an operator algebraic approach ⋮ Minimal index of a $C^{*}$-crossed product by a finite group ⋮ Coactions of a finite-dimensional $C^*$-Hopf algebra on unital $C^*$-algebras, unital inclusions of unital $C^*$-algebras and strong Morita equivalence ⋮ Realizations of rigid C*-tensor categories as bimodules over GJS C*-algebras ⋮ Rigid C*-Tensor Categories and their Realizations as Hilbert C*-Bimodules ⋮ Subalgebras of infinite \(C^*\)-algebras with finite Watatani indices. II: Cuntz-Krieger algebras ⋮ HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS ⋮ Imprimitivity bimodules of Cuntz–Krieger algebras and strong shift equivalences of matrices ⋮ Functor of points and height functions for noncommutative Arakelov geometry ⋮ Crossed products of Hilbert C*-bimodules by countable discrete groups ⋮ Maximal abelian subalgebras of \(C^\ast\)-algebras associated with complex dynamical systems and self-similar maps ⋮ Fundamental group of simple \(C^{*}\)-algebras with unique trace ⋮ On bicolimits of $ C^* $-categories ⋮ Subshifts, \(\lambda\)-graph bisystems and \(C^\ast\)-algebras ⋮ The \(\mathrm{C}^\ast\)-algebra index for observable algebra in non-equilibrium Hopf spin models ⋮ Lattice of intermediate subalgebras ⋮ Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital $C^*$-algebras

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