An intrinsic characterization of C*-simplicity
Operator Algebras
2018-10-22 v5 Group Theory
Abstract
A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.
Keywords
Cite
@article{arxiv.1509.01870,
title = {An intrinsic characterization of C*-simplicity},
author = {Matthew Kennedy},
journal= {arXiv preprint arXiv:1509.01870},
year = {2018}
}
Comments
18 pages; minor changes