Quantum Groups and Noncommutative Geometry

• Κύριος συγγραφέας: Manin, Yuri I. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 2nd ed. 2018.
• Σειρά: CRM Short Courses,
• Θέματα: Associative rings.; Rings (Algebra).; Group theory.; Category theory (Mathematics).; Homological algebra.; Associative Rings and Algebras.; Group Theory and Generalizations.; Category Theory, Homological Algebra.

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...

Πίνακας περιεχομένων:

• 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.