C*-simplicity has no local obstruction
Operator Algebras
2022-03-25 v2 Group Theory
Abstract
In 2016, I solved a problem of de la Harpe in 2006: Is there a non-discrete C*-simple group? However the solution was not fully satisfactory as the provided C*-simple groups (and their operator algebras) are very close to discrete groups. All previously known examples are of this form. In this article I give yet another construction of non-discrete C*-simple groups. The statement in the title then follows. This in particular gives the first examples of non-elementary C*-simple groups (in Wesolek's sense).
Cite
@article{arxiv.2103.10404,
title = {C*-simplicity has no local obstruction},
author = {Yuhei Suzuki},
journal= {arXiv preprint arXiv:2103.10404},
year = {2022}
}
Comments
Small corrections in the proofs of 2.1 and 4.1, other minor modifications, 9 pages, to appear in Forum of Mathematics, Sigma