On crossed products with property 𝑇

Watanabe, Shōichi

doi:10.1090/S0002-9939-1987-0877033-8

On crossed products with property $\textrm {T}$
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Proc. Amer. Math. Soc. 99 (1987), 647-650 Request permission

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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