Geodesic
On fusion categories
Pavel Etingof1 ; Dmitri Nikshych2 ; Viktor Ostrik3
1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
2 Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, United States
3 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States
Annals of mathematics, Tome 162 (2005) no. 2, pp. 581-642.

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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.
DOI : 10.4007/annals.2005.162.581

Pavel Etingof 1 ; Dmitri Nikshych 2 ; Viktor Ostrik 3

1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
2 Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, United States
3 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States 
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Pavel Etingof; Dmitri Nikshych; Viktor Ostrik. On fusion categories. Annals of mathematics, Tome 162 (2005) no. 2, pp. 581-642. doi : 10.4007/annals.2005.162.581. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.581/

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