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August 28, 2020

Compact Hypergroups from Discrete Subfactors

We show that to any local braided discrete subfactor N \subset M of type III one can associate a ”compact hypergroup” acting by extremal ucp maps on M, such that N is given by the fixed point algebra under this action. If the subfactor is also of depth two, then the hypergroup is exactly a compact group G and N is the fixed point under a minimal action of G. The motivation is to obtain an invariant and understand discrete inclusions of conformal nets. Based on joint work with Simone Del Vecchio, Luca Giorgetti (arXiv:2007.12384)