内容

目次

Introduction; 1. Poisson-Lie groups and Lie bialgebras; 2. CoboundaryPoisson-Lie groups and the classical Yang-Baxter equation; 3. Solutions ofthe classical Yang-Baxter equation; 4. Quasitriangular Hopf algebras; 5.Representations and quasitensor categories; 6. Quantization of Liebialgebras; 7. Quantized function algebras; 8. Structure of QUE algebras: theuniversal R-matrix; 9. Specializations of QUE algebras; 10. Representationsof QUE algebras: the generic case; 11. Representations of QUE algebras: theroot of unity case; 12. Infinite-dimensional quantum groups; 13. Quantumharmonic analysis; 14. Canonical bases; 15. Quantum group invariants of knotsand 3-manifolds; 16. Quasi-Hopf algebras and the Knizhnik-Zamolodchikovequation; Appendix. The Kac-Moody algebras.