Hopf Algebras and Congruence Subgroups
Rings and Algebras
2012-08-30 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Representation Theory
Abstract
We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra 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.
Cite
@article{arxiv.0710.0705,
title = {Hopf Algebras and Congruence Subgroups},
author = {Yorck Sommerhaeuser and Yongchang Zhu},
journal= {arXiv preprint arXiv:0710.0705},
year = {2012}
}
Comments
130 pages. Many new results added, remark by D. Nikshych included. See also http://www.southalabama.edu/mathstat/personal_pages/sommerh/