A characterization of $C^*$-simplicity of countable groups via Poisson boundaries
Dynamical Systems
2025-04-18 v1 Operator Algebras
Probability
Abstract
We characterize -simplicity for countable groups by means of the following dichotomy. If a group is -simple, then the action on the Poisson boundary is essentially free for a generic measure on the group. If a group is not -simple, then the action on the Poisson boundary is not essentially free for a generic measure on the group.
Cite
@article{arxiv.2504.13017,
title = {A characterization of $C^*$-simplicity of countable groups via Poisson boundaries},
author = {Andrei Alpeev},
journal= {arXiv preprint arXiv:2504.13017},
year = {2025}
}
Comments
This preprint superseds and expans upon my previous preprint arXiv:2409.02013