Algebra & Combinatorics Research Group  |  Texas A&M University





A&C Seminar

Working Seminar
   in Algebra

All Seminars

A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

October 3 Dmitri Nikshych (University of New Hampshire)
3:00–3:50 Weakly group-theoretical and solvable fusion categories
Abstract:   A fusion category (i.e., a finite semisimple tensor category) is called weakly group-theoretical (respectively, solvable) if it can be obtained by a certain iterative procedure using finite groups (respectively, cyclic groups). All known examples of semisimple (quasi-) Hopf algebras have weakly group-theoretical representation categories. We prove a categorical analogue of Burnside's theorem for finite groups, saying that a fusion category of dimension pnqm, where p and q are primes, is solvable. We also establish a Frobenius property of a weakly group-theoretical fusion category, i.e., that dimensions of simple objects of such a category C divide the dimension of C. We apply these results to classification of semisimple Hopf algebras of small dimension. (This is a joint work with P. Etingof and V. Ostrik.)