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A structural result of irreducible inclusions of type $\operatorname {III}_\lambda$ factors, $\lambda \in (0,1)$

Author: Phan H. Loi
Journal: Proc. Amer. Math. Soc. 126 (1998), 2651-2662
MSC (1991): Primary 46L10, 46L55
MathSciNet review: 1451818
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Abstract: Given an irreducible inclusion of factors with finite index $N\subset M$, where $M$ is of type ${III}_{\lambda ^{1/m}}$, $N$ of type ${III}_{\lambda ^{1/n}}$, $0<\lambda <1$, and $m,n$ are relatively prime positive integers, we will prove that if $N\subset M$ satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with $N\subset M$. Relations between $N\subset M$ and a certain $G$-kernel on subfactors are also discussed.

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Phan H. Loi
Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435

Received by editor(s): June 17, 1996
Received by editor(s) in revised form: January 28, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society