$\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912073261252608 |
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| author | Nawata, Norio |
| author_facet | Nawata, Norio |
| contents | We say that a countable discrete group action $α$ on a C$^*$-algebra $A$ is \textit{$\mathcal{W}$-absorbing} if there exist a C$^*$-algebra $B$ and an action $β$ on $B$ such that $α$ is cocycle conjugate to $β\otimes \mathrm{id}_{\mathcal{W}}$ on $B\otimes \mathcal{W}$ where $\mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we completely classify outer $\mathcal{W}$-absorbing actions of finite groups on $\mathcal{W}$ up to conjugacy and cocycle conjugacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra Nawata, Norio Operator Algebras Primary 46L55, Secondary 46L35, 46L40 We say that a countable discrete group action $α$ on a C$^*$-algebra $A$ is \textit{$\mathcal{W}$-absorbing} if there exist a C$^*$-algebra $B$ and an action $β$ on $B$ such that $α$ is cocycle conjugate to $β\otimes \mathrm{id}_{\mathcal{W}}$ on $B\otimes \mathcal{W}$ where $\mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we completely classify outer $\mathcal{W}$-absorbing actions of finite groups on $\mathcal{W}$ up to conjugacy and cocycle conjugacy. |
| title | $\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra |
| topic | Operator Algebras Primary 46L55, Secondary 46L35, 46L40 |
| url | https://arxiv.org/abs/2410.11213 |