Strongly outer actions of certain torsion-free amenable groups on the Razak-Jacelon algebra
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917839516991488 |
|---|---|
| author | Nawata, Norio |
| author_facet | Nawata, Norio |
| contents | Let $\mathfrak{C}$ be the smallest class of countable discrete groups with the following properties: (i) $\mathfrak{C}$ contains the trivial group, (ii) $\mathfrak{C}$ is closed under isomorphisms, countable increasing unions and extensions by $\mathbb{Z}$. Note that $\mathfrak{C}$ contains all countable discrete torsion-free abelian groups and poly-$\mathbb{Z}$ groups. Also, $\mathfrak{C}$ is a subclass of the class of countable discrete torsion-free elementary amenable groups. In this paper, we show that if $Γ\in \mathfrak{C}$, then all strongly outer actions of $Γ$ on the Razak-Jacelon algebra $\mathcal{W}$ are cocycle conjugate to each other. This can be regarded as an analogous result of Szabó's result for strongly self-absorbing C$^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strongly outer actions of certain torsion-free amenable groups on the Razak-Jacelon algebra Nawata, Norio Operator Algebras Primary 46L55, Secondary 46L35, 46L40 Let $\mathfrak{C}$ be the smallest class of countable discrete groups with the following properties: (i) $\mathfrak{C}$ contains the trivial group, (ii) $\mathfrak{C}$ is closed under isomorphisms, countable increasing unions and extensions by $\mathbb{Z}$. Note that $\mathfrak{C}$ contains all countable discrete torsion-free abelian groups and poly-$\mathbb{Z}$ groups. Also, $\mathfrak{C}$ is a subclass of the class of countable discrete torsion-free elementary amenable groups. In this paper, we show that if $Γ\in \mathfrak{C}$, then all strongly outer actions of $Γ$ on the Razak-Jacelon algebra $\mathcal{W}$ are cocycle conjugate to each other. This can be regarded as an analogous result of Szabó's result for strongly self-absorbing C$^*$-algebras. |
| title | Strongly outer actions of certain torsion-free amenable groups on the Razak-Jacelon algebra |
| topic | Operator Algebras Primary 46L55, Secondary 46L35, 46L40 |
| url | https://arxiv.org/abs/2309.00934 |