Finite Quantum Groupoids and Their Applications

Abstract

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.

44 pages, amslatex

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• Quantum groupoids
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• Exchange dynamical quantum groups
• Lectures on the dynamical Yang-Baxter equations
• A Galois correspondence for II_1 factors and quantum groupoids
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Cited by in corpus (33)

• Quantum groupoids
• Real Multiplication and noncommutative geometry
• Weak Hopf algebras and singular solutions of Quantum Yang-Baxter equation
• Categorification and correlation functions in conformal field theory
• Around the Hosszú-Gluskin theorem for $n$-ary groups
• Double categories and quantum groupoids
• Yetter-Drinfeld modules over weak Hopf algebras and the center construction
• Kitaev models based on unitary quantum groupoids
• Basic concepts of ternary Hopf algebras
• On fusion categories
• Partial compact quantum groups
• Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
• Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions
• Morita base change in quantum groupoids
• Inner Actions of Weak Hopf Algebras
• A few remarks on Pimsner-Popa bases and regular subfactors of depth 2
• A class of C*-algebraic locally compact quantum groupoids Part II: Main theory
• Deformation of finite dimensional C*-quantum groupoids
• Irreducible actions and compressible modules
• Kaplansky's Construction Type and Classification of Weak bialgebras and Weak Hopf algebras
• Algebraic structures in comodule categories over weak bialgebras
• C*-groupoides quantiques et inclusions de facteurs : Structure symetrique et autodualite, action sur le facteur hyperfini de type II1
• Regular multiplier Hopf algebroids II. Integration on and duality of algebraic quantum groupoids
• Actions and coactions of finite quantum groupoids on von Neumann algebras, extensions of the match pair procedure
• Partial $\ast$-algebraic quantum groups and Drinfeld doubles of partial compact quantum groups
• Projective representation theory for compact quantum groups and the quantum Baum-Connes assembly map
• Finite-dimensional Hopf C*-bimodules and C*-pseudo-multiplicative unitaries
• Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids
• Tensor categories attached to double groupoids
• A study of Blattner-Montgomery duality in weak Hopf algebras of groupoid algebras type
• Regular graded algebras and obstructed categories with duality
• Quantum direct products and the Künneth class
• Semisimple weak Hopf algebras