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...
| Autores: | , |
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| 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 |
| 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. |
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