A Quantum Groups Primer (Paperback)

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.