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

• Dmitri Nikshych ^[1]
  1. [1] University of New Hampshire

     University of New Hampshire

     Town of Durham, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 1, 2008, págs. 145-161
• Idioma: inglés
• DOI: 10.1007/s00029-008-0060-1
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• Resumen

  • 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 [7]. Namely, we show that certain Z /2 Z -equivariantizations of fusion categories constructed by D. Tambara and S. Yamagami [26] 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.