Quantum symmetries of noncommutative tori
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912179990560768 |
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| author | Evans, David E. Jones, Corey |
| author_facet | Evans, David E. Jones, Corey |
| contents | We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the $E_{8}$ subfactor on a noncommutative 3-torus, and of $\text{PSU}(2)_{15}$ on a noncommutative 4-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum symmetries of noncommutative tori Evans, David E. Jones, Corey Quantum Algebra Mathematical Physics Operator Algebras We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the $E_{8}$ subfactor on a noncommutative 3-torus, and of $\text{PSU}(2)_{15}$ on a noncommutative 4-torus. |
| title | Quantum symmetries of noncommutative tori |
| topic | Quantum Algebra Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2404.14466 |