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.
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
'... would serve admirably - as the author suggests - as the basis for a taught graduate course ... this book is a clearly written painless read. I can recommend this text as an entry work for those wishing to acquaint themselves with the still popular topic of quantum groups.' A. I. Solomon, Contemporary Physics 'Many intuitive comments and informal remarks, a well chosen set of main examples used systematically in the book and a clear and understandable style make the book very comfortable and useful for students as well as for mathematicians from other fields.' EMS Newsletter 'This monograph is an excellent reference (and often a true 'eye-opener') for researchers working in quantum groups ... S. Majid is well-known for his lively and very informative style of writing, and the reviewed book confirms this opinion. Thus the book is very well written, the proofs contain enough details to make them easily readable but still challenging enough to keep students interested ... I can full-heartily recommend this work as a basis for a one-term postgraduate course or as an introductory text to all mathematicians who would like to learn quickly the main ideas, techniques and wide range of applications of quantum group theory.' Zentralblatt MATH
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