On fusion rules and solvability of a fusion category

We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations o...

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Detalles Bibliográficos
Autores: Natale, Sonia Lujan, Escañuela Gonzalez, Melisa Gisselle
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/59792
Acceso en línea:http://hdl.handle.net/11336/59792
Access Level:acceso abierto
Palabra clave:fusion category
solvability
fusion rules
braided fusion category
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from representations of semisimple Hopf algebras associated to exact factorizations of the symmetric and alternating groups. In the context of spherical fusion categories, we also consider the invariant provided by the S-matrix of the Drinfeld center and show that this invariant does determine the solvability of a fusion category provided it is group-theoretical.