A Galois correspondence for II_1 factors and quantum groupoids

Abstract

We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a subfactor is completely and canonically determined by a quantum groupoid and its coideal *-subalgebra. This allows to express the bimodule category of a subfactor in terms of the representation category of a corresponding quantum groupoid and the principal graph as the Bratteli diagram of an inclusion of certain C^*-algebras related to it.

32 pages, Latex

References in corpus (2)

• Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers
• Doi-Hopf Modules over Weak Hopf Algebras

Cited by in corpus (10)

• Finite Quantum Groupoids and Their Applications
• A construction of finite index C*-algebra inclusions from free actions of compact quantum groups
• Dual Bialgebroids for Depth Two Ring Extensions
• Quantum Galois groups of subfactors
• Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions
• Morita base change in quantum groupoids
• On the structure of weak Hopf algebras
• C*-groupoides quantiques et inclusions de facteurs : Structure symetrique et autodualite, action sur le facteur hyperfini de type II1
• Tannaka-Krein reconstruction for coactions of finite quantum groupoids
• Algèbre combinatoire et effective: des graphes aux algèbres de Kac, via l'exploration informatique