内容

目次

Preface; 1. Coalgebras, bialgebras and Hopf algebras. Uq(b+); 2. Dualpairing. SLq(2). Actions; 3. Coactions. Quantum plane A2q; 4. Automorphismquantum groups; 5. Quasitriangular structures; 6. Roots of Unity. uq(sl2); 7.q-Binomials; 8. quantum double. Dual-quasitriangular structures; 9. Braidedcategories; 10 (Co)module categories. Crossed modules; 11. q-Hecke algebras;12. Rigid objects. Dual representations. Quantum dimension; 13. Knotinvariants; 14. Hopf algebras in braided categories; 15. Braideddifferentiation; 16. Bosonisation. Inhomogeneous quantum groups; 17. Doublebosonisation. Diagrammatic construction of uq(sl2); 18. The braided groupUq(n-). Construction of Uq(g); 19. q-Serre relations; 20. R-matrix methods;21. Group algebra, Hopf algebra factorisations. Bicrossproducts; 22. Liebialgebras. Lie splittings. Iwasawa decomposition; 23. Poisson geometry.Noncommutative bundles. q-Sphere; 24. Connections. q-Monopole. Nonuniversaldifferentials; Problems; Bibliography; Index.