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Hopf Algebras and Congruence Subgroups
Yorck Sommerhäuser, University of South Alabama, Mobile, AL, and Yongchang Zhu, Hong Kong University of Science & Technology, Kowloon, Hong Kong

Memoirs of the American Mathematical Society
2012; 134 pp; softcover
Volume: 219
ISBN-10: 0-8218-6913-2
ISBN-13: 978-0-8218-6913-0
List Price: US$72
Individual Members: US$43.20
Institutional Members: US$57.60
Order Code: MEMO/219/1028
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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 Frobenius-Schur 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 Frobenius-Schur 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
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