Examples of non-amenable, boundary-amenable dynamical systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913960319516672 |
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| author | Bassi, Jacopo |
| author_facet | Bassi, Jacopo |
| contents | It is proved that for every $r,s \in \mathbb{N}\backslash \{0,1\}$ the action of $\mathbb{F}_{r+s}$ on $\partial_β(\mathbb{F}_{r+s}/\mathbb{F}_r)$ is topologically amenable. In particular the $C^*$-algebra associated to the corresponding quasi-regular representation has a unique non-trivial ideal. The techniques involved rely on a study of dynamical properties for actions on non-standard boundaries studied by the author and F. R{\u a}dulescu in previous works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Examples of non-amenable, boundary-amenable dynamical systems Bassi, Jacopo Operator Algebras Group Theory 46L05 It is proved that for every $r,s \in \mathbb{N}\backslash \{0,1\}$ the action of $\mathbb{F}_{r+s}$ on $\partial_β(\mathbb{F}_{r+s}/\mathbb{F}_r)$ is topologically amenable. In particular the $C^*$-algebra associated to the corresponding quasi-regular representation has a unique non-trivial ideal. The techniques involved rely on a study of dynamical properties for actions on non-standard boundaries studied by the author and F. R{\u a}dulescu in previous works. |
| title | Examples of non-amenable, boundary-amenable dynamical systems |
| topic | Operator Algebras Group Theory 46L05 |
| url | https://arxiv.org/abs/2507.19614 |