A Quantum Groups Primer

Majid Shahn

170 pages, parution le 27/03/2002

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Résumé

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.

Contents

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Majid Shahn
Parution	27/03/2002
Nb. de pages	170
Format	15 x 22,7
Couverture	Broché
Poids	263g
Intérieur	Noir et Blanc
EAN13	9780521010412
ISBN13	978-0-521-01041-2