Hopf Algebras and Congruence Subgroups

We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.

• Author: Yorck Sommerhäuser, Yongchang Zhu
• Publisher: American Mathematical Soc.
• Published: 2012
• Pages: 146