Duality for actions of weak Kac algebras and crossed product inclusions of II_1 factors

Abstract

We show that indecomposable weak Kac algebras are free over their Cartan subalgebras and prove a duality theorem for their actions. Using this result, for any biconnected weak Kac algebra we construct a minimal action on the hyperfinite II_1 factor. The corresponding crossed product inclusion of II_1 factors has depth 2 and an integer index. Its first relative commutant is, in general, non-trivial, so we derive some arithmetic properties of weak Kac algebras from considering reduced subfactors.

Latex, 28 pages

References in corpus (3)

• Axioms for Weak Bialgebras
• Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers
• A characterization of depth 2 subfactors of II_1 factors

Cited by in corpus (8)

• Finite Quantum Groupoids and Their Applications
• Tannaka-Krein reconstruction and a characterization of modular tensor categories
• Quantum Galois groups of subfactors
• Invariants of Knots and 3-manifolds from Quantum Groupoids
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• C*-groupoides quantiques et inclusions de facteurs : Structure symetrique et autodualite, action sur le facteur hyperfini de type II1
• A characterization of depth 2 subfactors of II_1 factors
• Semisimple weak Hopf algebras