The representation category of any compact group is the bimodule category of a II_1 factor

Details The representation category of any compact group is the bimodule category of a II_1 factor The representation category of any compact group is the bimodule category of a II_1 factor

2008-11-11

arxiv.org/abs/0811.1764v4

Journal f\"ur die reine und angewandte Mathematik 643 (2010), 171-199

Mathematics

Operator Algebras

v4:Improved and more detailed exposition. No conceptual changes. Final version. v3:Correction to a technical assumption; clari

Scientific paper

We prove that given any compact group G, there exists a minimal action of G
on a II_1 factor M such that the bimodule category of the fixed-point II_1
factor M^G is naturally equivalent with the representation category of G. In
particular, all subfactors of M^G with finite Jones index can be described
explicitly.

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