C*-simplicity of free products with amalgamation and radical classes of groups
Operator Algebras
2017-12-01 v4 Group Theory
Abstract
We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a unique tracial state, but is not simple. Moreover, we show that there is a radical class of groups for which the reduced group C*-algebra of any group is simple precisely when the group has a trivial radical corresponding to this class.
Keywords
Cite
@article{arxiv.1605.06395,
title = {C*-simplicity of free products with amalgamation and radical classes of groups},
author = {Nikolay A. Ivanov and Tron Omland},
journal= {arXiv preprint arXiv:1605.06395},
year = {2017}
}
Comments
23 pages; the statement of Lemma 5.8 and the proof of Theorem 5.9 have been corrected, and certain paragraphs of Section 5 have been reformulated to accommodate for this