Realizing modular data from centers of near-group categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915217303142400 |
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| author | Yu, Zhiqiang Zhang, Qing |
| author_facet | Yu, Zhiqiang Zhang, Qing |
| contents | In this paper, we show the existence of a near-group category of type $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$ and compute the modular data of its Drinfeld center. We prove that a modular data of rank $10$ can be obtained through condensation of the Drinfeld center of the near-group category $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$, and it can also be realized as the Drinfeld center of a fusion category of rank $4$. Moreover, we compute the modular data for the Drinfeld center of a near-group category $\mathbb{Z} / 8\mathbb{Z}+8$ and show that the non-pointed factor of its condensation has the same modular data as the quantum group category $C(\mathfrak{g}_2, 4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Realizing modular data from centers of near-group categories Yu, Zhiqiang Zhang, Qing Quantum Algebra In this paper, we show the existence of a near-group category of type $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$ and compute the modular data of its Drinfeld center. We prove that a modular data of rank $10$ can be obtained through condensation of the Drinfeld center of the near-group category $\mathbb{Z} / 4\mathbb{Z} \times \mathbb{Z} / 4\mathbb{Z}+16$, and it can also be realized as the Drinfeld center of a fusion category of rank $4$. Moreover, we compute the modular data for the Drinfeld center of a near-group category $\mathbb{Z} / 8\mathbb{Z}+8$ and show that the non-pointed factor of its condensation has the same modular data as the quantum group category $C(\mathfrak{g}_2, 4)$. |
| title | Realizing modular data from centers of near-group categories |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2412.20763 |