Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2

We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases there are well-known examples of non-group-theoretical categories, coming from ce...

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Detalles Bibliográficos
Autores: Bruillard, Paul, Galindo, César, Hong, Seung Moon, Kashina, Yevgenia, Naidu, Deepak, Natale, Sonia Lujan, Plavnik, Julia Yael, Rowell, Eric C.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/20970
Acceso en línea:http://hdl.handle.net/11336/20970
Access Level:acceso abierto
Palabra clave:Fusion Category
Modular Category
Group-Theoretical Fusion Category
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. 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 4q^2 is equivalent to either one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.