Back to Search
Start Over
Property (T) for locally compact groups and C*-algebras
- Publication Year :
- 2018
-
Abstract
- Let $G$ be a locally compact group and let $C^*(G)$ and $C^*_r(G)$ be the full group $C^*$-algebra and the reduced group $C^*$-algebra of $G$. We investigate the relationship between Property $(T)$ for $G$ and Property $(T)$ as well as its strong version for $C^*(G)$ and $C^*_r(G)$. We show that $G$ has Property $(T)$ if (and only if) $C^*(G)$ has Property $(T)$. In the case where $G$ is a locally compact IN-group, we prove that $G$ has Property $(T)$ if and only if $C^*_r(G)$ has strong Property $(T)$. We also show that $C^*_r(G)$ has strong Property $(T)$ for every non-amenable locally compact group $G$ for which $C^*_r(G)$ is nuclear. Some of these groups (as for instance $G=SL_2(\mathbf{R})$) do not have Property $T$.<br />Comment: 9 pages
- Subjects :
- Mathematics - Operator Algebras
Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1803.10933
- Document Type :
- Working Paper