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

Academic Article


  • 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.
  • Status

    Publication Date

  • October 2008
  • Has Subject Area

    Published In


  • Fusion category
  • equivariantization
  • group-theoretical Hopf algebra
  • Digital Object Identifier (doi)

    Start Page

  • 145
  • End Page

  • 161
  • Volume

  • 14
  • Issue

  • 1