Computing fusion rules for spherical G-extensions of fusion categories

• Marcel Bischoff ^[1] ; Corey Jones ^[2]
  1. [1] Ohio University

     Ohio University

     Township of Athens, Estados Unidos

     
  2. [2] North Carolina State University

     North Carolina State University

     Township of Raleigh, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • A G-extension of a fusion category C yields a categorical action of G on the center Z(C). If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the action. We then apply this to find closed formulas for the fusion rules of extensions of some group theoretical categories and of cyclic permutation crossed extensions of modular categories.