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A characterization of normal extensions for subfactors

Author: Tamotsu Teruya
Journal: Proc. Amer. Math. Soc. 120 (1994), 781-783
MSC: Primary 46L37
MathSciNet review: 1207542
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Abstract: Let $ N \subset M \subset L$ be a tower of factors. If $ L$ is a crossed product $ N{ \rtimes _\alpha }G$ of $ N$ by an outer action $ \alpha $ of a finite group $ G$ on $ N$ then it is well known that there exists a subgroup $ H$ of $ G$ such that $ M = N{ \rtimes _{{\alpha _{{\vert _H}}}}}H$. We prove in this paper that $ H$ is a normal subgroup of $ G$ if and only if there exist a finite group $ F$ and an outer action $ \beta $ of $ F$ on $ M$ such that $ L = M{ \rtimes _\beta }F$.

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Keywords: Factor, outer action, crossed product, Galois theory, fixed point algebra, conditional expectation
Article copyright: © Copyright 1994 American Mathematical Society

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