GALOIS CORRESPONDENCES FOR SUBFACTORS RELATED TO NORMAL SUBGROUPS

Title & Authors
GALOIS CORRESPONDENCES FOR SUBFACTORS RELATED TO NORMAL SUBGROUPS
Lee, Jung-Rye;

Abstract
For an outer action $\small{\alpha}$ 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 $\small{\beta}$ of F on the crossed product algebra M $\small{\times}$$\small{_{\alpha}}$ G = (M $\small{\times}$$\small{_{\alpha}}$ F. We generalize this to infinite group actions. For an outer action $\small{\alpha}$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\small{\alpha}$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\small{\alpha}$ of a compact group G and a closed normal subgroup H, we prove $\small{M^{G}}$ = ( $\small{M^{H}}$)$\small{^{{beta}(G/H)}}$for a minimal action $\small{\beta}$ of G/H on $\small{M^{H}}$.f G/H on $\small{M^{H}}$.TEX> H/.
Keywords
Galois correspondence;crossed product algebra;fixed point algebra;cocycle crossed action;regular extension;
Language
English
Cited by
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