Memoirs of the American Mathematical Society 2012; 134 pp; softcover Volume: 219 ISBN10: 0821869132 ISBN13: 9780821869130 List Price: US$72 Individual Members: US$43.20 Institutional Members: US$57.60 Order Code: MEMO/219/1028
 The authors 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, they show that the projective kernel is a congruence subgroup. To do this, they introduce a class of generalized FrobeniusSchur indicators and endow it with an action of the modular group that is compatible with the original one. Table of Contents  Introduction
 The modular group
 Quasitriangular Hopf algebras
 Factorizable Hopf algebras
 The action of the modular group
 The semisimple case
 The case of the Drinfel'd double
 Induced modules
 Equivariant FrobeniusSchur indicators
 Two congruence subgroup theorems
 The action of the Galois group
 Galois groups and indicators
 Galois groups and congruence subgroups
 Notes
 Bibliography
 Subject index
 Symbol index
