Abstract
Abstract
In this article we initiate research on locally compact
\mathrm{C}^{*}
-simple groups. We first show that every
\mathrm{C}^{*}
-simple group must be totally disconnected. Then we study
\mathrm{C}^{*}
-algebras and von Neumann algebras associated with certain groups acting on trees. After formulating a locally compact analogue of Powers’ property, we prove that the reduced group
\mathrm{C}^{*}
-algebra of such groups is simple. This is the first simplicity result for
\mathrm{C}^{*}
-algebras of non-discrete groups and answers a question of de la Harpe. We also consider group von Neumann algebras of certain non-discrete groups acting on trees. We prove factoriality, determine their type and show non-amenability. We end the article by giving natural examples of groups satisfying the hypotheses of our work.
Subject
Applied Mathematics,General Mathematics
Reference62 articles.
1. The dual spaces of C*{\mathrm{C}^{*}}-algebras;Trans. Amer. Math. Soc.,1960
2. On simplcity of reduced C*{\mathrm{C}^{*}}-algebras of groups;Bull. Lond. Math. Soc.,2007
3. C*{\mathrm{C}^{*}}-simple groups: Amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds;J. Topol. Anal.,2011
4. Uncountably many II1\mathrm{II}_{1} factors;Ann. of Math. (2),1969
5. C*{\mathrm{C}^{*}}-algebras and Mackey’s theory of group representations;C*-algebras: 1943-1993,1994
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