A Galois correspondence for II₁ factors and quantum groupoids

2000/01/04 by Dmitri Nikshych, Leonid Vainerman
Mathematics · #math.QA #math.OA

paper · pdf

published as Journal of Func. Analysis, 178 no.1, 113-142 (2000) · 32 pages, Latex

arxiv created 2000/01/04 · arxiv updated 2009/11/30

Abstract

We establish a Galois correspondence for finite quantum groupoid actions on II₁ 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.

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• Algebraic Versions of a Finite-Dimensional Quantum Groupoid
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