Computably strongly self-absorbing C*-algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929518404435968 |
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| author | Goldbring, Isaac |
| author_facet | Goldbring, Isaac |
| contents | We introduce the notion of a computably strongly self-absorbing C*-algebra and show that the following C*-algebras are computably strongly self-absorbing: the Cuntz algebras $\mathcal{O}_2$ and $\mathcal{O}_\infty$, the UHF algebra $M_{\mathfrak{n}}(\mathbb{C})$ and the tensor product $M_{\mathfrak{n}}(\mathbb{C})\otimes \mathcal{O}_\infty$, where $\mathfrak{n}$ is a supernatural number of infinite type with computably enumerable support, and the Jiang-Su algebra $\mathcal{Z}$. In connection with the last example, we show that $\mathcal{Z}$ has a computable presentation. The results above are a special instance of a computable version of the standard approximate intertwining argument due to Elliott. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computably strongly self-absorbing C*-algebras Goldbring, Isaac Logic Operator Algebras We introduce the notion of a computably strongly self-absorbing C*-algebra and show that the following C*-algebras are computably strongly self-absorbing: the Cuntz algebras $\mathcal{O}_2$ and $\mathcal{O}_\infty$, the UHF algebra $M_{\mathfrak{n}}(\mathbb{C})$ and the tensor product $M_{\mathfrak{n}}(\mathbb{C})\otimes \mathcal{O}_\infty$, where $\mathfrak{n}$ is a supernatural number of infinite type with computably enumerable support, and the Jiang-Su algebra $\mathcal{Z}$. In connection with the last example, we show that $\mathcal{Z}$ has a computable presentation. The results above are a special instance of a computable version of the standard approximate intertwining argument due to Elliott. |
| title | Computably strongly self-absorbing C*-algebras |
| topic | Logic Operator Algebras |
| url | https://arxiv.org/abs/2409.18834 |