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arXiv · 0712.0585

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

Dmitri Nikshych
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Abstract

Given 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.

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Dmitri Nikshych. 2007-12-04. Non group-theoretical semisimple Hopf algebras from group actions on fusion categories. https://arxiv.org/abs/0712.0585

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