Selfless inclusions arising from commensurator groups of hyperbolic groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911677310566400 |
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| author | Basu, Aaratrick Flores, Felipe |
| author_facet | Basu, Aaratrick Flores, Felipe |
| contents | We provide new examples of $\mathrm{C}^*$-selfless groups and inclusions. In particular, we prove that the commensurator group ${\rm Comm}(H)$ of a torsion-free hyperbolic group $H$ is $\mathrm{C}^*$-selfless. Our approach involves showing that the Gromov boundary $\partial H$ is a topologically free extreme boundary for ${\rm Comm}(H)$, ${\rm Aut}(H)$, and for other groups that contain $H$ in an almost normal way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12737 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Selfless inclusions arising from commensurator groups of hyperbolic groups Basu, Aaratrick Flores, Felipe Group Theory Operator Algebras Primary 22D25, Secondary 20F67, 46L05, 37B05 We provide new examples of $\mathrm{C}^*$-selfless groups and inclusions. In particular, we prove that the commensurator group ${\rm Comm}(H)$ of a torsion-free hyperbolic group $H$ is $\mathrm{C}^*$-selfless. Our approach involves showing that the Gromov boundary $\partial H$ is a topologically free extreme boundary for ${\rm Comm}(H)$, ${\rm Aut}(H)$, and for other groups that contain $H$ in an almost normal way. |
| title | Selfless inclusions arising from commensurator groups of hyperbolic groups |
| topic | Group Theory Operator Algebras Primary 22D25, Secondary 20F67, 46L05, 37B05 |
| url | https://arxiv.org/abs/2605.12737 |