Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909253866881024 |
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| author | Fang, Xiaochun Wang, Zhongli |
| author_facet | Fang, Xiaochun Wang, Zhongli |
| contents | Let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, let $G$ be a finite group, and let $α\colon G\rightarrow \mathrm{Aut}(A)$ be an action of $G$ on $A$ which has the weak tracial Rokhlin property. We prove that if $A$ has property (TM), then the crossed product $A\rtimes_αG$ has property (TM). As a corollary, if $A$ is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, $α\colon G\rightarrow \mathrm{Aut}(A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then $A\rtimes_αG$ has stable rank one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property Fang, Xiaochun Wang, Zhongli Operator Algebras Let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, let $G$ be a finite group, and let $α\colon G\rightarrow \mathrm{Aut}(A)$ be an action of $G$ on $A$ which has the weak tracial Rokhlin property. We prove that if $A$ has property (TM), then the crossed product $A\rtimes_αG$ has property (TM). As a corollary, if $A$ is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, $α\colon G\rightarrow \mathrm{Aut}(A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then $A\rtimes_αG$ has stable rank one. |
| title | Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2407.09867 |