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arXiv · 2312.12195

On the center of near-group fusion category of type $\mathbb{Z}_3+6$

Zhiqiang Yu
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Abstract

Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\mathcal{Z}(\mathcal{A})\cong\mathcal{C}(\mathbb{Z}_3,\eta)\boxtimes\mathcal{C}(\mathfrak{sl}_3,9)_{\mathbb{Z}_3}^0$. 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.

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Zhiqiang Yu. 2023-12-19. On the center of near-group fusion category of type $\mathbb{Z}_3+6$. https://arxiv.org/abs/2312.12195

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