Non-C*-simple groups admit non-free actions on their Poisson boundaries
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929484487196672 |
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| author | Alpeev, Andrei |
| author_facet | Alpeev, Andrei |
| contents | It is a classical result of Kaimanovich and Vershik and independently of Rosenblatt that a non-amenable group admits a non-degenerate symmetric measure such that the Poisson boundary is trivial. Most if not all examples to date of non-free actions of countable groups on their Poisson boundaries had the stabilizers sitting inside the amenable radical. We show that every countable non-C*-simple group admits a symmetric measure of full support with non-trivial stabilizers. For a class of non-C*-simple groups with trivial amenable radical, which is non-empty as was shown by le Boudec, this gives a wealth of examples with non-normal stabilizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-C*-simple groups admit non-free actions on their Poisson boundaries Alpeev, Andrei Group Theory Dynamical Systems Operator Algebras Probability It is a classical result of Kaimanovich and Vershik and independently of Rosenblatt that a non-amenable group admits a non-degenerate symmetric measure such that the Poisson boundary is trivial. Most if not all examples to date of non-free actions of countable groups on their Poisson boundaries had the stabilizers sitting inside the amenable radical. We show that every countable non-C*-simple group admits a symmetric measure of full support with non-trivial stabilizers. For a class of non-C*-simple groups with trivial amenable radical, which is non-empty as was shown by le Boudec, this gives a wealth of examples with non-normal stabilizers. |
| title | Non-C*-simple groups admit non-free actions on their Poisson boundaries |
| topic | Group Theory Dynamical Systems Operator Algebras Probability |
| url | https://arxiv.org/abs/2409.02013 |