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

Fuente: arXiv
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Main Author: Yu, Zhiqiang
Format: Preprint
Published: 2023
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_version_ 1866909062360203264
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