C*simplicity of locally compact Powers groups
Abstract
In this article we initiate research on locally compact C*simple groups. We first show that every C*simple group must be totally disconnected. Then we study 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 C*algebra of such groups is simple. This is the first simplicity result for C*algebras of nondiscrete groups and answers a question of de la Harpe. We also consider group von Neumann algebras of certain nondiscrete groups acting on trees. We prove factoriality, determine their type and show nonamenability. We end the article by giving natural examples of groups satisfying the hypotheses of our work.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.07793
 Bibcode:
 2015arXiv150507793R
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Group Theory;
 Mathematics  Representation Theory;
 22D25;
 46L05;
 46L10;
 20C07;
 20C08
 EPrint:
 32 pages, v2: accepted for publication in J. Reine Angew. Math.