Centers of graded fusion categories

Academic Article


  • Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center Z(C) of C is shown to be canonically equivalent to a G-equivariantization of the relative center Z_D(C). We use this result to obtain a criterion for C to be group-theoretical and apply it to Tambara-Yamagami fusion categories. We also find several new series of modular categories by analyzing the centers of Tambara-Yamagami categories. Finally, we prove a general result about existence of zeroes in S-matrices of weakly integral modular categories.
  • Authors

  • Gelaki, Shlomo
  • Naidu, Deepak
  • Nikshych, Dmitri
  • Status

    Publication Date

  • 2009
  • Has Subject Area

    Published In


  • braided categories
  • fusion categories
  • graded tensor categories
  • Digital Object Identifier (doi)

    Start Page

  • 959
  • End Page

  • 990
  • Volume

  • 3
  • Issue

  • 8