Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2

We classify integral modular categories of dimension pq4 and p2q2, where p and q are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension 4q2. In these cases there are well-known examples of non-group-theoretical categories, coming from cente...

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Autores principales:	Bruillard, Paul, Galindo Martínez, César Neyit, Hong, Seung-Moon, Kashina, Yevgenia, Naidu, Deepak, Natale, Sonia Luján, Plavnik, Julia Yael, Rowell, Eric C.
Formato:	article
Lenguaje:	Inglés
Publicado:	2022
Materias:	Modular categories Fusion categories Frobenius–Perron dimension Group-theoretical
Acceso en línea:	http://hdl.handle.net/11086/29853 https://doi.org/10.48550/arXiv.1303.4748
Aporte de:	Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba

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institution	Universidad Nacional de Córdoba
institution_str	I-10
repository_str	R-141
collection	Repositorio Digital Universitario (UNC)
language	Inglés
topic	Modular categories Fusion categories Frobenius–Perron dimension Group-theoretical
spellingShingle	Modular categories Fusion categories Frobenius–Perron dimension Group-theoretical Bruillard, Paul Galindo Martínez, César Neyit Hong, Seung-Moon Kashina, Yevgenia Naidu, Deepak Natale, Sonia Luján Plavnik, Julia Yael Rowell, Eric C. Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
topic_facet	Modular categories Fusion categories Frobenius–Perron dimension Group-theoretical
description	We classify integral modular categories of dimension pq4 and p2q2, where p and q are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension 4q2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara–Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q2 is either equivalent to one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.
format	article
author	Bruillard, Paul Galindo Martínez, César Neyit Hong, Seung-Moon Kashina, Yevgenia Naidu, Deepak Natale, Sonia Luján Plavnik, Julia Yael Rowell, Eric C.
author_facet	Bruillard, Paul Galindo Martínez, César Neyit Hong, Seung-Moon Kashina, Yevgenia Naidu, Deepak Natale, Sonia Luján Plavnik, Julia Yael Rowell, Eric C.
author_sort	Bruillard, Paul
title	Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
title_short	Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
title_full	Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
title_fullStr	Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
title_full_unstemmed	Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
title_sort	classification of integral modular categories of frobenius–perron dimension pq4 and p2q2
publishDate	2022
url	http://hdl.handle.net/11086/29853 https://doi.org/10.48550/arXiv.1303.4748
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Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2

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