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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the existence of central sequences in subfactors


Author: Dietmar H. Bisch
Journal: Trans. Amer. Math. Soc. 321 (1990), 117-128
MSC: Primary 46L35
DOI: https://doi.org/10.1090/S0002-9947-1990-1005075-5
MathSciNet review: 1005075
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Abstract: We prove a relative version of [Co1, Theorem 2.1] for a pair of type ${\text {I}}{{\text {I}}_1}$-factors $N \subset M$. This gives a list of necessary and sufficient conditions for the existence of nontrivial central sequences of $M$ contained in the subfactor $N$. As an immediate application we obtain a result by Bédos [Be, Theorem A], showing that if $N$ has property $\Gamma$ and $G$ is an amenable group acting freely on $N$ via some action $\sigma$, then the crossed product $N{ \times _\sigma }G$ has property $\Gamma$. We also include a proof of a relative Mc Duff-type theorem (see [McD, Theorems $1$, $2$ and $3$]), which gives necessary and sufficient conditions implying that the pair $N \subset M$ is stable.


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Article copyright: © Copyright 1990 American Mathematical Society