Finite quantum groupoids

DOI10.1006/jabr.2000.8610zbMath1003.46040OpenAlexW2091109133MaRDI QIDQ5942793

Jean-Michel Vallin

Publication date: 9 September 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2000.8610

zbMATH Keywords

subfactorsdepth-2 inclusions of von Neumann algebrasmultipicative partial isometriespseudo-multiplicative unitariesquantum groupoids

Mathematics Subject Classification ID

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

Related Items (9)

The unitary implementation of a measured quantum groupoid action ⋮ Outer actions of measured quantum groupoids ⋮ Bialgebroid actions on depth two extensions and duality. ⋮ Actions and coactions of finite quantum groupoids on von Neumann algebras, extensions of the matched pair procedure ⋮ A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition ⋮ Inclusions of von Neumann algebras and quantum groupoïds. III ⋮ Pseudo-multiplicative unitaries associated with inclusions of finite-dimensional \(C^*\)-algebras ⋮ Yetter-Drinfel'd algebras and coideals of Weak Hopf $C^*$-Algebras ⋮ A class of \(C^\ast\)-algebraic locally compact quantum groupoids. II: Main theory

Cites Work

• A groupoid approach to C*-algebras
• Irreducible inclusions of factors and multiplicative unitaries
• Duality for generalized Kac algebras and a characterization of finite groupoid algebras
• Inclusions of von Neumann algebras, and quantum groupoïds
• Index for subfactors
• A Galois correspondence for \(II_1\) factors and quantum groupoids
• Irreducible inclusions of factors, multiplicative unitaries, and Kac algebras
• Weak Hopf algebras. I: Integral theory and \(C^*\)-structure
• A characterization of depth 2 subfactors of II\(_1\) factors
• A coassociative \(C^*\)-quantum group with nonintegral dimensions
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• Index for 𝐶*-subalgebras
• HOPF ALGEBROIDS AND QUANTUM GROUPOIDS
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