Simplicity of $C^*$-algebras of contracting self-similar groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Gardella, Eusebio Nekrashevych, Volodymyr Steinberg, Benjamin Vdovina, Alina |
| author_facet | Gardella, Eusebio Nekrashevych, Volodymyr Steinberg, Benjamin Vdovina, Alina |
| contents | We show that the $C^*$-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex $\ast$-algebra is simple. We also improve on Steinberg and Szakać's algorithm to determine if the $\ast$-algebra is simple. This provides an interesting class of non-Hausdorff amenable, effective and minimal ample groupoids for which simplicity of the $C^*$-algebra and the complex $\ast$-algebra are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplicity of $C^*$-algebras of contracting self-similar groups Gardella, Eusebio Nekrashevych, Volodymyr Steinberg, Benjamin Vdovina, Alina Operator Algebras Group Theory 46L99, 20F65, 20F10 We show that the $C^*$-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex $\ast$-algebra is simple. We also improve on Steinberg and Szakać's algorithm to determine if the $\ast$-algebra is simple. This provides an interesting class of non-Hausdorff amenable, effective and minimal ample groupoids for which simplicity of the $C^*$-algebra and the complex $\ast$-algebra are equivalent. |
| title | Simplicity of $C^*$-algebras of contracting self-similar groups |
| topic | Operator Algebras Group Theory 46L99, 20F65, 20F10 |
| url | https://arxiv.org/abs/2501.11482 |