A quantum groups primer
著者
書誌事項
A quantum groups primer
（London Mathematical Society lecture note series, 292）
Cambridge University Press, 2002
- : pbk
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注記
Bibliography: p. 166
Includes index
内容説明・目次
内容説明
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists.
目次
- Preface
- 1. Coalgebras, bialgebras and Hopf algebras. Uq(b+)
- 2. Dual pairing. SLq(2). Actions
- 3. Coactions. Quantum plane A2q
- 4. Automorphism quantum groups
- 5. Quasitriangular structures
- 6. Roots of Unity. uq(sl2)
- 7. q-Binomials
- 8. quantum double. Dual-quasitriangular structures
- 9. Braided categories
- 10 (Co)module categories. Crossed modules
- 11. q-Hecke algebras
- 12. Rigid objects. Dual representations. Quantum dimension
- 13. Knot invariants
- 14. Hopf algebras in braided categories
- 15. Braided differentiation
- 16. Bosonisation. Inhomogeneous quantum groups
- 17. Double bosonisation. Diagrammatic construction of uq(sl2)
- 18. The braided group Uq(n-). Construction of Uq(g)
- 19. q-Serre relations
- 20. R-matrix methods
- 21. Group algebra, Hopf algebra factorisations. Bicrossproducts
- 22. Lie bialgebras. Lie splittings. Iwasawa decomposition
- 23. Poisson geometry. Noncommutative bundles. q-Sphere
- 24. Connections. q-Monopole. Nonuniversal differentials
- Problems
- Bibliography
- Index.
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