GALOIS CORRESPONDENCES FOR SUBFACTORS RELATED TO NORMAL SUBGROUPS Lee, Jung-Rye;
For an outer action 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 of F on the crossed product algebra M G = (M F. We generalize this to infinite group actions. For an outer action of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action of a compact group G and a closed normal subgroup H, we prove = ( )for a minimal action of G/H on .f G/H on .TEX> H/.
Galois correspondence;crossed product algebra;fixed point algebra;cocycle crossed action;regular extension;