Hopf Algebras and Congruence Subgroups

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.

130 pages. Many new results added, remark by D. Nikshych included. See also http://www.southalabama.edu/mathstat/personal_pages/sommerh/

Cited by in corpus (10)

• Congruence Property In Conformal Field Theory
• Congruence Subgroups and Generalized Frobenius-Schur Indicators
• On classification of modular tensor categories
• Twisted Frobenius-Schur indicators for Hopf algebras
• Tensor categories: A selective guided tour
• The logarithmic Cardy case: Boundary states and annuli
• Eigenvalues of rotations and braids in spherical fusion categories
• On the Central Charge of a Factorizable Hopf Algebra
• Clifford group is not a semidirect product in dimensions $N$ divisible by four
• Frobenius-Schur Indicators and the Mapping Class Group of the Torus