Quantum Groups and Noncommutative Geometry

  • Yuri I. Manin

Part of the CRM Short Courses book series (CRMSC)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Yuri I. Manin
    Pages 1-3
  3. Yuri I. Manin
    Pages 11-17
  4. Yuri I. Manin
    Pages 37-41
  5. Yuri I. Manin
    Pages 43-46
  6. Yuri I. Manin
    Pages 67-71
  7. Yuri I. Manin
    Pages 79-81
  8. Theo Raedschelders, Michel Van den Bergh
    Pages 83-115
  9. Back Matter
    Pages 117-125

About this book


This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others.  This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.


quantum groups Hopf algebras Tanaka-Krein coalgebras bialgebras monoidal categories noncommutative geometry Yuri Manin textbook

Authors and affiliations

  • Yuri I. Manin
    • 1
  1. 1.Max Planck Institute for MathematicsBonnGermany

Bibliographic information