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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17709 |
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| _version_ | 1866929652871725056 |
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| author | Spielberg, Jack |
| author_facet | Spielberg, Jack |
| contents | We solve the isomorphism problem for essential unital $C^*$-algebra extensions of the form $0 \to \mathcal{K} \oplus \mathcal{K} \to E \xrightarrowπ M_n \otimes C(\mathbb{T}) \to 0$. We then relate these to analogs of the Effros Shen AF algebras for rational numbers. This involves $C^*$-algebras constructed from categories of paths built from certain nonsimple continued fraction expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^*$-algebra extensions associated to continued fraction expansions of rational numbers Spielberg, Jack Operator Algebras We solve the isomorphism problem for essential unital $C^*$-algebra extensions of the form $0 \to \mathcal{K} \oplus \mathcal{K} \to E \xrightarrowπ M_n \otimes C(\mathbb{T}) \to 0$. We then relate these to analogs of the Effros Shen AF algebras for rational numbers. This involves $C^*$-algebras constructed from categories of paths built from certain nonsimple continued fraction expansions. |
| title | $C^*$-algebra extensions associated to continued fraction expansions of rational numbers |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2405.17709 |