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Hopf Algebras and Congruence Subgroups
 
Yorck Sommerhäuser University of South Alabama, Mobile, AL
Yongchang Zhu Hong Kong University of Science & Technology, Kowloon, Hong Kong
Hopf Algebras and Congruence Subgroups
eBook ISBN:  978-0-8218-9108-7
Product Code:  MEMO/219/1028.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
Hopf Algebras and Congruence Subgroups
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Hopf Algebras and Congruence Subgroups
Yorck Sommerhäuser University of South Alabama, Mobile, AL
Yongchang Zhu Hong Kong University of Science & Technology, Kowloon, Hong Kong
eBook ISBN:  978-0-8218-9108-7
Product Code:  MEMO/219/1028.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2192012; 134 pp
    MSC: Primary 16; Secondary 17

    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
     
     
    • Chapters
    • Introduction
    • 1. The Modular Group
    • 2. Quasitriangular Hopf Algebras
    • 3. Factorizable Hopf Algebras
    • 4. The Action of the Modular Group
    • 5. The Semisimple Case
    • 6. The Case of the Drinfel’d Double
    • 7. Induced Modules
    • 8. Equivariant Frobenius-Schur Indicators
    • 9. Two Congruence Subgroup Theorems
    • 10. The Action of the Galois Group
    • 11. Galois Groups and Indicators
    • 12. Galois Groups and Congruence Subgroups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2192012; 134 pp
MSC: Primary 16; Secondary 17

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.

  • Chapters
  • Introduction
  • 1. The Modular Group
  • 2. Quasitriangular Hopf Algebras
  • 3. Factorizable Hopf Algebras
  • 4. The Action of the Modular Group
  • 5. The Semisimple Case
  • 6. The Case of the Drinfel’d Double
  • 7. Induced Modules
  • 8. Equivariant Frobenius-Schur Indicators
  • 9. Two Congruence Subgroup Theorems
  • 10. The Action of the Galois Group
  • 11. Galois Groups and Indicators
  • 12. Galois Groups and Congruence Subgroups
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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