C*-simplicity and the amenable radical
Group Theory
2016-11-01 v4 Operator Algebras
Abstract
A countable group is C*-simple if its reduced C*-algebra is simple. It is well known that C*-simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.
Keywords
Cite
@article{arxiv.1507.03452,
title = {C*-simplicity and the amenable radical},
author = {Adrien Le Boudec},
journal= {arXiv preprint arXiv:1507.03452},
year = {2016}
}
Comments
The previous versions of this article were entitled "Discrete groups that are not C*-simple". The results have been strengthened and Theorem D has been added