On the center of near-group fusion category of type $\mathbb{Z}_3+6$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909062360203264 |
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| author | Yu, Zhiqiang |
| author_facet | Yu, Zhiqiang |
| contents | Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\mathcal{Z}(\mathcal{A})\cong\mathcal{C}(\mathbb{Z}_3,η)\boxtimes\mathcal{C}(\mathfrak{sl}_3,9)_{\mathbb{Z}_3}^0$. Moreover, we construct two non-trivial faithful extensions of $\mathcal{A}$ explicitly, whose Drinfeld centers can also be obtained from representation categories quantum groups at root of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12195 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the center of near-group fusion category of type $\mathbb{Z}_3+6$ Yu, Zhiqiang Quantum Algebra Category Theory Rings and Algebras 18M20, 81R50 Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\mathcal{Z}(\mathcal{A})\cong\mathcal{C}(\mathbb{Z}_3,η)\boxtimes\mathcal{C}(\mathfrak{sl}_3,9)_{\mathbb{Z}_3}^0$. Moreover, we construct two non-trivial faithful extensions of $\mathcal{A}$ explicitly, whose Drinfeld centers can also be obtained from representation categories quantum groups at root of unity. |
| title | On the center of near-group fusion category of type $\mathbb{Z}_3+6$ |
| topic | Quantum Algebra Category Theory Rings and Algebras 18M20, 81R50 |
| url | https://arxiv.org/abs/2312.12195 |