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On the center of near-group fusion category of type $\mathbb{Z}_3+6$ (2312.12195v4)
Published 19 Dec 2023 in math.QA, math.CT, and math.RA
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.