Subalgebras of infinite \(C^*\)-algebras with finite Watatani indices. II: Cuntz-Krieger algebras

DOI10.1215/S0012-7094-98-09118-9zbMath0949.46023MaRDI QIDQ1974785

Masaki Izumi

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Markov tracesbraided endomorphismsbiunitary connections on finite graphsbraid symmetryCuntz algebras with finite Watatani indicesCuntz-Krieger algebras with finite Watatani indexinfinite-depth caseinfinite-dimensional Kac algebrasunitary representations of the braid group

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Subfactors and their classification (46L37)

Related Items (22)

Q-system completion for \(C^\ast 2\)-categories ⋮ Centrally free actions of amenable \(\mathrm{C}^*\)-tensor categories on von Neumann algebras ⋮ Complete descriptions of intermediate operator algebras by intermediate extensions of dynamical systems ⋮ Unnamed Item ⋮ Anomalous symmetries of classifiable C*-algebras ⋮ The Nakayama automorphism of the almost Calabi-Yau algebras associated to \(\mathrm{SU}(3)\) modular invariants ⋮ C*-algebras from planar algebras I: Canonical C*-algebras associated to a planar algebra ⋮ Visualizing Automorphisms of Graph Algebras ⋮ CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS ⋮ \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories ⋮ Coactions of a finite-dimensional $C^*$-Hopf algebra on unital $C^*$-algebras, unital inclusions of unital $C^*$-algebras and strong Morita equivalence ⋮ SUBFACTOR REALIZATION OF MODULAR INVARIANTS: II ⋮ Remarks on anomalous symmetries of \(C^*\)-algebras ⋮ Endomorphisms of graph algebras ⋮ THE STRUCTURE OF SECTORS ASSOCIATED WITH LONGO–REHREN INCLUSIONS II: EXAMPLES ⋮ ON A SUBFACTOR ANALOGUE OF THE SECOND COHOMOLOGY ⋮ A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras ⋮ Ideal structure and simplicity of the \(C^*\)-algebras generated by Hilbert bimodules ⋮ Computations of Turaev-Viro-Ocneanu Invariants of 3-Manifolds from Subfactors ⋮ Subalgebras of infinite \(C^*\)-algebras with finite Watatani indices. I: Cuntz algebras ⋮ On graphC*-algebras ⋮ Lattice of intermediate subalgebras

Cites Work

• Unnamed Item
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• Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
• Extension of Jones' theory on index of arbitrary factors
• Duals of compact Lie groups realized in the Cuntz algebras and their actions on \(C^ *\)-algebras
• Compact matrix pseudogroups
• Hecke algebras of type \(A_ n\) and subfactors
• Metaplectic link invariants
• A class of C*-algebras and topological Markov chains
• K-theory for certain C*-algebras
• Application of fusion rules to classification of subfactors
• A remark on the minimal index of subgfactors
• Minimal index and braided subfactors
• Simple \(C^*\)-algebras generated by isometries
• Subalgebras of infinite \(C^*\)-algebras with finite Watatani indices. I: Cuntz algebras
• A duality for Hopf algebras and for subfactors. I
• Goldman's type theorem for index 3
• Spin models on finite cyclic groups
• Orbifold subfactors from Hecke algebras
• A generalization of the Cuntz algebras and model actions
• A theory of dimension
• Fourier transform for paragroups and its application to the depth two case
• Simple injective subfactors
• Minimizing indices of conditional expectations onto a subfactor
• Index of subfactors and statistics of quantum fields. I
• Superselection sectors with braid group statistics and exchange algebras
• Index for subfactors
• On flatness of Ocneanu's connections of the Dynkin diagrams and classification of subfactors
• Classification of amenable subfactors of type II
• Classification of Cuntz-Krieger algebras
• Classification of certain infinite simple \(C^*\)-algebras
• Classification of paragroup actions on subfactors
• Irreducible inclusions of factors, multiplicative unitaries, and Kac algebras
• Paragroup of Adrian Ocneanu and Kac algebra
• Classification of subfactors with the principal graph \(D^{(1)}_ n\)
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• Index for 𝐶*-subalgebras
• Entropy and index for subfactors
• The Crossed Product of a C ∗ -Algebra by an Endomorphism
• Representations of finite groups and Cuntz-Krieger algebras
• Finite Index Subfactors and Hopf Algebra Crossed Products
• A NOTE ON OCNEANU'S APPROACH TO JONES' INDEX THEORY
• Jones index theory by Hilbert C*-bimodules and K-theory

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