Proximality and selflessness for group C*-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910161137827840 |
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| author | Ozawa, Narutaka |
| author_facet | Ozawa, Narutaka |
| contents | We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic groups with no nontrivial finite normal subgroups and all Zariski-dense subgroups of PSL(n,R), are selfless in the sense of L. Robert. This generalizes the recent results of Amrutam, Gao, Kunnawalkam Elayavalli, and Patchell, and of Vigdorovich. We also prove that selflessness is stable under tensor product among exact C*-algebras and that a C*-probability space is selfless provided that it is either simple and purely infinite or simple, exact, Z-stable, and uniquely tracial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proximality and selflessness for group C*-algebras Ozawa, Narutaka Operator Algebras Dynamical Systems Functional Analysis Primary 37B05, Secondary 46L35 We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic groups with no nontrivial finite normal subgroups and all Zariski-dense subgroups of PSL(n,R), are selfless in the sense of L. Robert. This generalizes the recent results of Amrutam, Gao, Kunnawalkam Elayavalli, and Patchell, and of Vigdorovich. We also prove that selflessness is stable under tensor product among exact C*-algebras and that a C*-probability space is selfless provided that it is either simple and purely infinite or simple, exact, Z-stable, and uniquely tracial. |
| title | Proximality and selflessness for group C*-algebras |
| topic | Operator Algebras Dynamical Systems Functional Analysis Primary 37B05, Secondary 46L35 |
| url | https://arxiv.org/abs/2508.07938 |