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تسجيل مستخدم جديدExistence of tracial states on reduced group C*-algebras
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Let $G$ be a locally compact group. It is not always the case that its reduced C*-algebra $C^*_r(G)$ admits a tracial state. We exhibit closely related necessary and sufficient conditions for the existence of such. We gain a complete answer when $G$ compactly generated. In particular for $G$ almost connected, or more generally when $C^*_r(G)$ is nuclear, the existence of a trace is equivalent to amenability. We exhibit two examples of classes of totally disconnected groups for which $C^*_r(G)$ does not admit a tracial state.
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