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 grouptheoretical and solvable fusion categories 

Abstract: A fusion category (i.e., a finite semisimple tensor category) is called weakly grouptheoretical (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 grouptheoretical representation categories. We prove a categorical analogue of Burnside's theorem for finite groups, saying that a fusion category of dimension p^{n}q^{m}, where p and q are primes, is solvable. We also establish a Frobenius property of a weakly grouptheoretical 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.) 

