A Galois correspondence for II_1 factors and quantum groupoids

Details A Galois correspondence for II_1 factors and quantum groupoids A Galois correspondence for II_1 factors and quantum groupoids

2000-01-04

arxiv.org/abs/math/0001020v1

Journal of Func. Analysis, 178 no.1, 113-142 (2000)

Mathematics

Quantum Algebra

32 pages, Latex

Scientific paper

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.

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