Symmetric Flat Connections, Triviality of Loi's Invariant and Orbifold Subfactors

Abstract

We define a notion of symmetric connections on subfactors and get a sufficient condition for a subfactor to have a symmetric connection. We also give a necessary and sufficient condition for Loi's invariant of a non-strongly outer automorphism of a subfactor to be trivial in the case with a symmetric connection. We apply this result to non-AFD SU(_n_k subfactors and construct orbifold subfactors of non-AFD SU(_n_k subfactors as well as the AFD case, as conjectured in our previous work. This generalizes constructions of Evans-Kawahigashi and Xu.