Inclusions of von Neumann algebras, and quantum groupoïds

DOI10.1006/jfan.1999.3520zbMath0974.46055OpenAlexW4213139592MaRDI QIDQ1567414

Jean-Michel Vallin, Michel Enock

Publication date: 4 September 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3520

zbMATH Keywords

von Neumann algebraspseudo-multiplicative unitaryHopf bimodulesquantum groupoïdscrossed-productoperator-valued weightco-actions

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) General theory of von Neumann algebras (46L10) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in quantum physics (46N50) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items

Measured quantum transformation groupoids ⋮ The unitary implementation of a measured quantum groupoid action ⋮ Relative matched pairs of finite groups from depth two inclusions of von Neumann algebras to quantum groupoids ⋮ Outer actions of measured quantum groupoids ⋮ A planar calculus for infinite index subfactors ⋮ Comonoidal W\(^*\)-Morita equivalence for von Neumann bialgebras ⋮ Actions and coactions of finite quantum groupoids on von Neumann algebras, extensions of the matched pair procedure ⋮ Pseudo-multiplicative unitaries on \(C^*\)-modules and Hopf \(C^*\)-families. I. ⋮ Weak Hopf algebras. II: Representation theory, dimensions, and the Markov trace ⋮ Inclusions of von Neumann algebras and quantum groupoïds. III ⋮ Finite quantum groupoids ⋮ Pseudo-multiplicative unitaries associated with inclusions of finite-dimensional \(C^*\)-algebras ⋮ Measured quantum groupoids associated with matched pairs of locally compact groupoids ⋮ C*-pseudo-multiplicative unitaries, Hopf C*-bimodules and their Fourier algebras ⋮ Inclusions of von Neumann algebras and quantum groupoids. II

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