Uniform property $Γ$ for Crossed products by group actions with the Rokhlin-type properties
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915357029040128 |
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| author | Fang, Xiaochun Tian, Haotian |
| author_facet | Fang, Xiaochun Tian, Haotian |
| contents | In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a second-countable compact group which has the tracial Rokhlin property with comparison. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform property $Γ$ for Crossed products by group actions with the Rokhlin-type properties Fang, Xiaochun Tian, Haotian Operator Algebras Primary 46L55, Secondary 46L35 In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a second-countable compact group which has the tracial Rokhlin property with comparison. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$. |
| title | Uniform property $Γ$ for Crossed products by group actions with the Rokhlin-type properties |
| topic | Operator Algebras Primary 46L55, Secondary 46L35 |
| url | https://arxiv.org/abs/2412.10486 |