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)