• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.99-110
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• 1999

We apply sector theory to obtain some characterization on Gaois groups for subfactors. As an example of a non-irreducible inclusion of small index, a locally trivial inclusion arising from an automorphism is considered and its Galois group is completely determined by using sector theory.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.253-260
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• 2002

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