Amenable tensor categories and their realizations as AFD bimodules

DOI10.1006/jfan.1999.3521zbMath0996.46025OpenAlexW1965615329MaRDI QIDQ1976332

Shigeru Yamagami, Tomohiro Hayashi

Publication date: 10 April 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3521

zbMATH Keywords

bimodulessubfactorsamenabilityminimal actionFrobenius dualityTensor categoryAFD \(II_1\) factoramenable dualsbimodule realization of tensor categoriesclassification of amenable subfactors of type IIcrossed products in bimodulesfully faithful imbeding

Mathematics Subject Classification ID

(C^*)-modules (46L08) Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Subfactors and their classification (46L37) Classifications of (C^*)-algebras (46L35) Tensor products of (C^*)-algebras (46L06)

Related Items

Bicommutant categories from fusion categories ⋮ Classification of minimal actions of a compact Kac algebra with amenable dual ⋮ A planar algebraic description of conditional expectations ⋮ Classification of outer actions of discrete amenable groupoids on injective factors ⋮ Actions of groups and quantum groups on amenable factors ⋮ Amenability of groupoids and asymptotic invariance of convolution powers ⋮ Centrally free actions of amenable \(\mathrm{C}^*\)-tensor categories on von Neumann algebras ⋮ Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles ⋮ Braided categories of endomorphisms as invariants for local quantum field theories ⋮ Poisson boundaries of monoidal categories ⋮ Haploid algebras in \(C^*\)-tensor categories and the Schellekens list ⋮ Generalized orbifold construction for conformal nets ⋮ Realization of rigid \(C^\ast \)-bicategories as bimodules over type \(\mathrm{II}_1\) von Neumann algebras ⋮ Howe–Moore type theorems for quantum groups and rigid -tensor categories ⋮ CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS ⋮ Realizations of rigid C*-tensor categories as bimodules over GJS C*-algebras ⋮ Rigid C*-Tensor Categories and their Realizations as Hilbert C*-Bimodules ⋮ Motzkin algebras and the An tensor categories of bimodules ⋮ Non-unitary fusion categories and their doubles via endomorphisms ⋮ Non-commutative Poisson boundaries and compact quantum group actions ⋮ Classification of Roberts actions of strongly amenable C∗-tensor categories on the injective factor of type III₁ ⋮ Harmonic function spaces of probability measures on fusion algebras ⋮ Irreducibility of the wysiwyg representations of Thompson's groups ⋮ Description of the automorphism group \(\text{Aut}({\mathcal A}/{\mathcal A}^\alpha)\) for a minimal action of a compact Kac algebra and its application ⋮ Tannaka duals in semisimple tensor categories ⋮ Rigid C*-tensor categories of bimodules over interpolated free group factors ⋮ C\(^*\)-tensor categories and free product bimodules ⋮ A remark on CFT realization of quantum doubles of subfactors: case index \(<4\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extension of Jones' theory on index of arbitrary factors
• \(W^ *\)-categories
• Compact matrix pseudogroups
• Random walks on discrete groups: Boundary and entropy
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Produit croise d'une algebre de von Neumann par une algebre de Kac. II
• Minimal index and braided subfactors
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Produit croise d'une algebre de von Neumann par une algebre de Kac
• A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras
• A minimal action of the compact quantum group \(SU_q(n)\) on a full factor
• The Connes spectrum for actions of compact Kac algebras and factoriality of their crossed products
• Algebraic aspects in modular theory
• Modular theory for bimodules
• A theory of dimension
• Classification of subfactors: The reduction to commuting squares
• Minimizing indices of conditional expectations onto a subfactor
• Index for subfactors
• A von Neumann algebra framework for the duality of the quantum groups
• On unitary representation theories of compact quantum groups
• Classification of amenable subfactors of type II
• An axiomatization of the lattice of higher relative commutants of a subfactor
• Crossed products in bimodules
• Amenability of Hopf von Neumann algebras and Kac algebras
• Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property \(T\)
• Notes on amenability of commutative fusion algebras
• FACTORIALITY OF HARMONIC TRACES ON STRING ALGEBRAS
• Entropy and index for subfactors
• II 1 Factors, Their Bimodules and Hypergroups
• AMENABILITY AND STRONG AMENABILITY FOR FUSION ALGEBRAS WITH APPLICATIONS TO SUBFACTOR THEORY
• AN ANALOGUE OF PASCHKE'S THEOREM FOR ACTIONS OF COMPACT KAC ALGEBRAS
• CONSTRUCTION OF AN OUTER ACTION OF A FINITE-DIMENSIONAL KAC ALGEBRA ON THE AFD FACTOR OF TYPE II₁
• A NOTE ON OCNEANU'S APPROACH TO JONES' INDEX THEORY
• Frobenius Reciprocity in Tensor Categories
• The Multiplicativity of the Minimal Index of Simple C ∗ -Algebras
• Composition of subfactors : new examples of infinite depth subfactors