On fusion categories

• Autores: Pavel Etingof, Victor Ostrik, Dimitri Nickshych
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 2, 2005, págs. 581-642
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.581
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• Resumen

  • 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 (not necessarily hermitian) modular category 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. At the end of the paper we generalize some of these results to positive characteristic.