On fusion categories

Details On fusion categories On fusion categories

2002-03-07

arxiv.org/abs/math/0203060v10

Mathematics

Quantum Algebra

50 pages, latex; a reference to Schauenburg's freeness theorem was added and a new section 5.11 to fill a gap in the previous

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On fusion categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On fusion categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On fusion categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-583480