GALOIS CORRESPONDENCES FOR SUBFACTORS RELATED TO NORMAL SUBGROUPS

Abstract

For an outer action fi of a finite group G on a factor M, it was proved that H is a normal subgroup of G if and only if there exists a finite group F and an outer action fl of F on the crossed product algebra Mofi H with Mofi G » (Mofi H)ofl F. We generalize this to infinite group actions. For an outer action fi of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When fi satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action fi of a compact group G and a closed normal subgroup H, we prove M G = (M H ) fl(G=H) for a minimal action fl of G=H on M H.