On the classification of weakly integral modular categories
type: Item
instance of: scholarly article
title: On the classification of weakly integral modular categories
zbMATH Open document ID: 1332.18011
author: Paul Bruillard
author: César Galindo
author: Siu-Hung Ng
author: Eric C. Rowell
author: Zhenghan Wang
author: Julia Yael Plavnik
published in: Journal of Pure and Applied Algebra
publication date: 2016-02-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.2313
review text: The aim of this paper is to classify all modular categories of dimension \(4m\), where \(m\) is an odd square-free integer, and all ranks \(6\) and \(7\) weakly integral modular categories. More precisely, the main result establishes that, if \(\mathcal C\) is a weakly integral modular category either of \(rank \leq 7\) or with Frobenius-Perron dimension \(4m\), where \(m\) is an odd square-free integer, then \(\mathcal C\) is equivalent to a (Deligne) product of the following: pointed categories, Ising categories and metaplectic categories.
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 6539224
reviewed by: J. N. Alonso Alvarez
MaRDI profile type: Publication
OpenAlex ID: W2963037390
arXiv ID: 1411.2313
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DOI: 10.1016/J.JPAA.2015.11.010
description: scientific article