Strongly outer actions of certain torsionfree amenable groups on the RazakJacelon algebra
Abstract
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 torsionfree abelian groups and poly$\mathbb{Z}$ groups. Also, $\mathfrak{C}$ is a subclass of the class of countable discrete torsionfree elementary amenable groups. In this paper, we show that if $\Gamma\in \mathfrak{C}$, then all strongly outer actions of $\Gamma$ on the RazakJacelon algebra $\mathcal{W}$ are cocycle conjugate to each other. This can be regarded as an analogous result of Szabó's result for strongly selfabsorbing C$^*$algebras.
 Publication:

arXiv eprints
 Pub Date:
 September 2023
 DOI:
 10.48550/arXiv.2309.00934
 arXiv:
 arXiv:2309.00934
 Bibcode:
 2023arXiv230900934N
 Keywords:

 Mathematics  Operator Algebras;
 Primary 46L55;
 Secondary 46L35;
 46L40
 EPrint:
 8 pages, I have changed Definition 2.2