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Klappentext Here is a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists. Zusammenfassung Presents a self-contained introduction to quantum groups as algebraic objects. Aimed as a primer for mathematicians! the book will also be useful for mathematical physicists. It is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. Inhaltsverzeichnis 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.
