On inner-amenability and boundary actions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910813048012800 |
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| author | Bassi, Jacopo |
| author_facet | Bassi, Jacopo |
| contents | Let $Γ$ be a discrete countable group. The first main result of this work is that if $Γ$ is ICC inner-amenable non-amenable then it cannot satisfy the (AO)-property, answering a question posed by C. Anantharaman-Delaroche. It is also proved that if $Γ$ is a "sufficiently large" discrete subgroup of a product of locally compact second countable bi-exact groups, then it cannot be inner-amenable. Both these results generalize the well-known fact that ICC non-amenable inner-amenable discrete countable groups cannot be bi-exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inner-amenability and boundary actions Bassi, Jacopo Operator Algebras Group Theory 20E34 (Primary) 37A55, 46L05 (Secondary) Let $Γ$ be a discrete countable group. The first main result of this work is that if $Γ$ is ICC inner-amenable non-amenable then it cannot satisfy the (AO)-property, answering a question posed by C. Anantharaman-Delaroche. It is also proved that if $Γ$ is a "sufficiently large" discrete subgroup of a product of locally compact second countable bi-exact groups, then it cannot be inner-amenable. Both these results generalize the well-known fact that ICC non-amenable inner-amenable discrete countable groups cannot be bi-exact. |
| title | On inner-amenability and boundary actions |
| topic | Operator Algebras Group Theory 20E34 (Primary) 37A55, 46L05 (Secondary) |
| url | https://arxiv.org/abs/2410.01447 |