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Quantum Groups and Noncommutative Geometry

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...

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Bibliographic Details
Main Author: Manin, Yuri I.
Format: eBook
Language:English
Published: Cham Springer International Publishing 2018, 2018
Edition:2nd ed. 2018
Series:CRM Short Courses
Subjects:
Associative Rings And Algebras
Homological Algebra
Group Theory
Rings (algebra)
Associative Rings
Category Theory, Homological Algebra
Group Theory And Generalizations
Category Theory (mathematics)
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 1. The Quantum Group GL(2)
  • 2. Bialgebras and Hopf Algebras
  • 3. Quadratic Algebras as Quantum Linear Spaces
  • 4. Quantum Matrix Spaces. I. Categorical Viewpoint
  • 5. Quantum Matrix Spaces. II. Coordinate Approach
  • 6. Adding Missing Relations
  • 7. From Semigroups to Groups
  • 8. Frobenius Algebras and the Quantum Determinant
  • 9. Koszul Complexes and the Growth Rate of Quadratic Algebras
  • 10. Hopf *-Algebras and Compact Matrix Pseudogroups
  • 11. Yang-Baxter Equations
  • 12. Algebras in Tensor Categories and Yang-Baxter Functors
  • 13. Some Open Problems
  • 14. The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups
  • Bibliography
  • Index

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