A structural result of irreducible inclusions of type 𝐼𝐼𝐼_{𝜆} factors, 𝜆∈(0,1)

Loi, Phan

doi:10.1090/S0002-9939-98-04349-4

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

Proc. Amer. Math. Soc. 126 (1998), 2651-2662

DOI: https://doi.org/10.1090/S0002-9939-98-04349-4

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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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