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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Bibliographische Detailangaben
1. Verfasser: Manin, Yuri I. (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:2nd ed. 2018.
Schriftenreihe:CRM Short Courses,
Schlagworte:
Associative rings.
Rings (Algebra).
Group theory.
Category theory (Mathematics).
Homological algebra.
ISBN:9783319979878
ISSN:2522-5200
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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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