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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On crossed products with property $ {\rm T}$


Author: Shōichi Watanabe
Journal: Proc. Amer. Math. Soc. 99 (1987), 647-650
MSC: Primary 46L55; Secondary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1987-0877033-8
MathSciNet review: 877033
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Abstract: Let $ N$ be a finite von Neumann algebra (with faithful normal normalized trace $ \tau $), $ G$ a countable discrete group, and $ \alpha $ a $ \tau $-preserving action of $ G$ on $ N$ such that $ N{ \rtimes _\alpha }G$ is a factor. It is proved that if $ N{ \rtimes _\alpha }G$ has Property $ {\text{T}}$, then $ G$ has Kazhdan's Property $ {\text{T}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0877033-8
Keywords: Crossed product, Property $ {\text{T}}$
Article copyright: © Copyright 1987 American Mathematical Society

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