English

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

R2 v1 2026-06-22T10:50:19.817Z