On fusion categories

Academic Article


  • Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any modular category (not necessarily hermitian) is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity). In particular the number of such categories (functors) realizing a given fusion datum is finite. Finally, we develop the theory of Frobenius-Perron dimensions in an arbitrary fusion category and classify categories of prime dimension.
  • Authors

  • Etingof, P
  • Nikshych, Dmitri
  • Ostrik, V
  • Status

    Publication Date

  • September 2005
  • Has Subject Area

    Published In


  • math.QA
  • Digital Object Identifier (doi)

    Start Page

  • 581
  • End Page

  • 642
  • Volume

  • 162
  • Issue

  • 2