Every finite C*-tensor category is the bimodule category of a II_1 factor

Details Every finite C*-tensor category is the bimodule category of a II_1 factor Every finite C*-tensor category is the bimodule category of a II_1 factor

2011-12-17

arxiv.org/abs/1112.4088v1

Mathematics

Operator Algebras

22 pages

Scientific paper

We prove that given any finite C*-tensor category C, there exists an uncountable family of pairwise non stably isomorphic II_1 factors (M_i) such that the bimodule category of M_i is equivalent to C for all i. In particular, every finite C*-tensor category is the bimodule category of a II_1 factor. As an application we prove the existence of a II_1 factor for which the set of indices of finite index irreducible subfactors is $\{1, \frac{5 + \sqrt{13}}{2}, 12 + 3\sqrt{13}, 4 + \sqrt{13}, \frac{11 + 3\sqrt{13}}{2}, \frac{13 + 3\sqrt{13}}{2}, \frac{19 + 5\sqrt{13}}{2}, \frac{7 + \sqrt{13}}{2} \}$.

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