Lie Algebras of Finite and Affine Type

摘要: 1. Basic concepts 2. Representations of soluble and nilpotent Lie algebras 3. Cartan subalgebras 4. The decomposition 5. root systems the Weyl group 6. matrix Dynkin diagram 7. existence uniqueness theorems 8. simple 9. Some universal constructions 10. Irreducible modules for semisimple 11. Further properties enveloping algebra 12. Character dimension formulae 13. Fundamental 14. Generalized matrices Kac-Moody 15. classification generalised 16 invariant form, system 17. affine type 18. Realisations 19. representations symmetrisable 20. 21. Borcherds Appendix.