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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Detalles Bibliográficos
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
id I10-R141-11086-29853
record_format dspace
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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