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A Galois Correspondence for II1 Factors and Quantum Groupoids

✍ Scribed by Dmitri Nikshych; Leonid Vainerman

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 273 KB
Volume: 178
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3650

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✦ Synopsis

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 subfactor is completely and canonically determined by a quantum groupoid and its coideal V-subalgebra. This allows us 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 finite-dimensional C*-algebras related to it.

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