$\mathcal{Z}$-stability for $\mathrm C^*$-algebras of minimal line-bundle-twisted homeomorphisms with the small boundary property
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917101448462336 |
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| author | Forough, Marzieh Jeong, Ja A Strung, Karen R. |
| author_facet | Forough, Marzieh Jeong, Ja A Strung, Karen R. |
| contents | In this paper we show that the Cuntz--Pimsner algebras associated to minimal homeomorphisms twisted by line bundles, along with their orbit-breaking subalgebras, are $\mathcal{Z}$-stable whenever the underlying dynamical system has the small boundary property. This entails that this class is classified by the Elliott invariant. Furthermore, we show that the tensor product of two such $\mathrm{C}^*$-algebras is always $\mathcal{Z}$-stable, without assuming the small boundary property. In particular this applies to $\mathrm{C}^*$-algebras arising from systems with positive mean dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{Z}$-stability for $\mathrm C^*$-algebras of minimal line-bundle-twisted homeomorphisms with the small boundary property Forough, Marzieh Jeong, Ja A Strung, Karen R. Operator Algebras Dynamical Systems 46L35, 46L85, 46H25, 37B05 In this paper we show that the Cuntz--Pimsner algebras associated to minimal homeomorphisms twisted by line bundles, along with their orbit-breaking subalgebras, are $\mathcal{Z}$-stable whenever the underlying dynamical system has the small boundary property. This entails that this class is classified by the Elliott invariant. Furthermore, we show that the tensor product of two such $\mathrm{C}^*$-algebras is always $\mathcal{Z}$-stable, without assuming the small boundary property. In particular this applies to $\mathrm{C}^*$-algebras arising from systems with positive mean dimension. |
| title | $\mathcal{Z}$-stability for $\mathrm C^*$-algebras of minimal line-bundle-twisted homeomorphisms with the small boundary property |
| topic | Operator Algebras Dynamical Systems 46L35, 46L85, 46H25, 37B05 |
| url | https://arxiv.org/abs/2511.19387 |