Title: Hopf Algebras, Equivariant Frobenius-Schur Indicators, and Congruence Subgroups
Abstract: Ideas coming from conformal field theory lead in particular to an action of the modular group on the center of a semisimple factorizable Hopf algebra. We explain why the kernel of this action is a congruence subgroup, which implies that the action factors over a finite group. An important tool in this proof, which we will also describe in the talk, are the equivariant Frobenius-Schur indicators, a generalization of the ordinary Frobenius-Schur indicators that are equivariant with respect to the action of the modular group.