Non group-theoretical semisimple Hopf algebras from group actions on fusion categories

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dc.creatorNikshych, Dmitri
dc.date2007-12-04
dc.date.accessioned2026-07-07T13:15:44Z
dc.date.available2026-07-07T13:15:44Z
dc.descriptionGiven an action of a finite group G on a fusion category C we give a criterion for the category of G-equivariant objects in C to be group-theoretical, i.e., to be categorically Morita equivalent to a category of group-graded vector spaces. We use this criterion to answer affirmatively the question about existence of non group-theoretical semisimple Hopf algebras asked by P. Etingof, V. Ostrik, and the author in math/0203060. Namely, we show that certain Z/2Z-equivariantizations of fusion categories constructed by D. Tambara and S. Yamagami are equivalent to representation categories of non group-theoretical semisimple Hopf algebras. We describe these Hopf algebras as extensions and show that they are upper and lower semisolvable.
dc.descriptionLaTeX, 15 pages
dc.identifierhttps://arxiv.org/abs/0712.0585
dc.identifierhttp://arxiv.org/abs/0712.0585
dc.identifierSelecta Math. 14 (2008), 145-161.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230563
dc.subjectQuantum Algebra
dc.titleNon group-theoretical semisimple Hopf algebras from group actions on fusion categories
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