A characterization of $C^*$-simplicity of countable groups via Poisson boundaries
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910913515225088 |
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| author | Alpeev, Andrei |
| author_facet | Alpeev, Andrei |
| contents | We characterize $C^*$-simplicity for countable groups by means of the following dichotomy. If a group is $C^*$-simple, then the action on the Poisson boundary is essentially free for a generic measure on the group. If a group is not $C^*$-simple, then the action on the Poisson boundary is not essentially free for a generic measure on the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of $C^*$-simplicity of countable groups via Poisson boundaries Alpeev, Andrei Dynamical Systems Operator Algebras Probability We characterize $C^*$-simplicity for countable groups by means of the following dichotomy. If a group is $C^*$-simple, then the action on the Poisson boundary is essentially free for a generic measure on the group. If a group is not $C^*$-simple, then the action on the Poisson boundary is not essentially free for a generic measure on the group. |
| title | A characterization of $C^*$-simplicity of countable groups via Poisson boundaries |
| topic | Dynamical Systems Operator Algebras Probability |
| url | https://arxiv.org/abs/2504.13017 |