Realizing modular data from centers of near-group categories

Fuente: arXiv
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Main Authors: Yu, Zhiqiang, Zhang, Qing
Format: Preprint
Published: 2024
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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