On the small boundary property, $\mathcal Z$-absorption, and Bauer simplexes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910903088185344 |
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| author | Elliott, George A. Niu, Zhuang |
| author_facet | Elliott, George A. Niu, Zhuang |
| contents | Let $X$ be a compact metrizable space, and let $Δ$ be a closed set of Borel probability measures on $X$. We study the small boundary property of the pair $(X, Δ)$. In particular, it is shown that $(X, Δ)$ has the small boundary property if it has a restricted version of property Gamma.
As an application, it is shown that, if $A$ is the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^d$, where $(X, \mathbb Z^d)$ is a free minimal topological dynamical system, or if $A$ is an AH algebra with diagonal maps, then, $A$ is $\mathcal Z$-stable if the set of extreme tracial states is compact, regardless of its dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the small boundary property, $\mathcal Z$-absorption, and Bauer simplexes Elliott, George A. Niu, Zhuang Operator Algebras Dynamical Systems Let $X$ be a compact metrizable space, and let $Δ$ be a closed set of Borel probability measures on $X$. We study the small boundary property of the pair $(X, Δ)$. In particular, it is shown that $(X, Δ)$ has the small boundary property if it has a restricted version of property Gamma. As an application, it is shown that, if $A$ is the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^d$, where $(X, \mathbb Z^d)$ is a free minimal topological dynamical system, or if $A$ is an AH algebra with diagonal maps, then, $A$ is $\mathcal Z$-stable if the set of extreme tracial states is compact, regardless of its dimension. |
| title | On the small boundary property, $\mathcal Z$-absorption, and Bauer simplexes |
| topic | Operator Algebras Dynamical Systems |
| url | https://arxiv.org/abs/2406.09748 |