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 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.
Keywords
Cite
@article{arxiv.1505.07793,
title = {C*-simplicity of locally compact Powers groups},
author = {Sven Raum},
journal= {arXiv preprint arXiv:1505.07793},
year = {2016}
}
Comments
32 pages, v2: accepted for publication in J. Reine Angew. Math.; title changed; simpler proof of Theorem 6.1; typos corrected