Examples of non-amenable, boundary-amenable dynamical systems

Fuente: arXiv
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Main Author: Bassi, Jacopo
Format: Preprint
Published: 2025
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author Bassi, Jacopo
author_facet Bassi, Jacopo
contents It is proved that for every $r,s \in \mathbb{N}\backslash \{0,1\}$ the action of $\mathbb{F}_{r+s}$ on $\partial_β(\mathbb{F}_{r+s}/\mathbb{F}_r)$ is topologically amenable. In particular the $C^*$-algebra associated to the corresponding quasi-regular representation has a unique non-trivial ideal. The techniques involved rely on a study of dynamical properties for actions on non-standard boundaries studied by the author and F. R{\u a}dulescu in previous works.
format Preprint
id arxiv_https___arxiv_org_abs_2507_19614
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Examples of non-amenable, boundary-amenable dynamical systems
Bassi, Jacopo
Operator Algebras
Group Theory
46L05
It is proved that for every $r,s \in \mathbb{N}\backslash \{0,1\}$ the action of $\mathbb{F}_{r+s}$ on $\partial_β(\mathbb{F}_{r+s}/\mathbb{F}_r)$ is topologically amenable. In particular the $C^*$-algebra associated to the corresponding quasi-regular representation has a unique non-trivial ideal. The techniques involved rely on a study of dynamical properties for actions on non-standard boundaries studied by the author and F. R{\u a}dulescu in previous works.
title Examples of non-amenable, boundary-amenable dynamical systems
topic Operator Algebras
Group Theory
46L05
url https://arxiv.org/abs/2507.19614