Stable rank one, tracial local homogeneity and uniform property $Γ$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918479149400064 |
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| author | Vaccaro, Andrea |
| author_facet | Vaccaro, Andrea |
| contents | We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $Γ$. In particular, Villadsen algebras of the first type and crossed products of free minimal actions of FC (in particular, abelian) groups on compact metric spaces have uniform property $Γ$. This implies that all these C*-algebras satisfy the Toms-Winter conjecture, a fact already known for C*-algebras with stable rank one and locally finite nuclear dimension, and here recovered via a different approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24682 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable rank one, tracial local homogeneity and uniform property $Γ$ Vaccaro, Andrea Operator Algebras We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $Γ$. In particular, Villadsen algebras of the first type and crossed products of free minimal actions of FC (in particular, abelian) groups on compact metric spaces have uniform property $Γ$. This implies that all these C*-algebras satisfy the Toms-Winter conjecture, a fact already known for C*-algebras with stable rank one and locally finite nuclear dimension, and here recovered via a different approach. |
| title | Stable rank one, tracial local homogeneity and uniform property $Γ$ |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2604.24682 |