A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909605703974912 |
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| author | Castillejos, Jorge Debets, Baukje Szabo, Gabor |
| author_facet | Castillejos, Jorge Debets, Baukje Szabo, Gabor |
| contents | We show that two simple, separable, nuclear and $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the UCT and can be viewed as a tracial stably projectionless analog of the homotopy rigidity theorem for Kirchberg algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras Castillejos, Jorge Debets, Baukje Szabo, Gabor Operator Algebras 46L55, 46L05 We show that two simple, separable, nuclear and $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the UCT and can be viewed as a tracial stably projectionless analog of the homotopy rigidity theorem for Kirchberg algebras. |
| title | A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras |
| topic | Operator Algebras 46L55, 46L05 |
| url | https://arxiv.org/abs/2505.04857 |