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Property $T$ of reduced $C^*$-crossed products by discrete groups
- Source :
- Ann. Funct. Anal. 7, no. 3 (2016), 381-385
- Publication Year :
- 2015
-
Abstract
- We generalize the main result of Kamalov and show that if $G$ is an amenable discrete group with an action $\alpha$ on a finite nuclear unital $C^*$-algebra $A$ such that the reduced crossed product $A\rtimes_{\alpha,r} G$ has property $T$, then $G$ is finite and $A$ is finite dimensional. As an application, an infinite discrete group $H$ is non-amenable if and only if the uniform Roe algebra $C^*_u(H)$ has property $T$.
- Subjects :
- Mathematics - Operator Algebras
Subjects
Details
- Database :
- arXiv
- Journal :
- Ann. Funct. Anal. 7, no. 3 (2016), 381-385
- Publication Type :
- Report
- Accession number :
- edsarx.1511.03397
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1215/20088752-3605762