A Galois correspondence for \(II_1\) factors and quantum groupoids

DOI10.1006/jfan.2000.3650zbMath0995.46041arXivmath/0001020OpenAlexW1987227394MaRDI QIDQ1840772

Leonid Vainerman, Dmitri Nikshych

Publication date: 15 October 2002

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

Full work available at URL: https://arxiv.org/abs/math/0001020

zbMATH Keywords

crossed productprincipal graphBratelli diagrambasic constructioncategory of \(N\)-\(N\)-bimodulesfinite \(C^*\)-quantum groupoidinclusions of factorsleft coideals involutive subalgebrasquantum groupoids actionsweak Hopf \(C^*\)-algebra

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Subfactors and their classification (46L37)

Related Items (27)

Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2 ⋮ Quantum Galois groups of subfactors ⋮ Depth one extensions of semisimple algebras and Hopf subalgebras. ⋮ Fuzzy \(n\)-ary subpolygroups. ⋮ Isomorphisms of hypergroups and of \(n\)-hypergroups with applications. ⋮ Semilattices of simple and regular \(n\)-ary semigroups ⋮ Relative matched pairs of finite groups from depth two inclusions of von Neumann algebras to quantum groupoids ⋮ (Co)homology of crossed products by weak Hopf algebras ⋮ Representation theory of polyadic groups. ⋮ Bialgebroid actions on depth two extensions and duality. ⋮ On a problem about tensor products of subfactors ⋮ On a subfactor generalization of Wall's conjecture ⋮ Morita equivalence for weak Hopf–Galois extensions ⋮ Actions and coactions of finite quantum groupoids on von Neumann algebras, extensions of the matched pair procedure ⋮ Fuzzy subgroups of \(n\)-ary subgroups. ⋮ A theory of induction and classification of tensor \(C^\ast\)-categories ⋮ Finite depth and Jacobson-Bourbaki correspondence. ⋮ Finitary Galois extensions over noncommutative bases. ⋮ Finite quantum groupoids ⋮ Ergodic actions of \(S_\mu U(2)\) on \(C^{*}\)-algebras from \(II_{1}\) subfactors ⋮ Frobenius extensions and weak Hopf algebras ⋮ Generalized symmetry in noncommutative (complex) geometry ⋮ Classifying (weak) coideal subalgebras of weak Hopf \(C^\ast \)-algebras ⋮ Yetter-Drinfel'd algebras and coideals of Weak Hopf $C^*$-Algebras ⋮ EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS ⋮ On the structure of weak Hopf algebras ⋮ Invariants of knots and 3-manifolds from quantum groupoids

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• A characterization of depth 2 subfactors of II\(_1\) factors
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