Lie Algebras, Part 2: Finite and Infinite Dimensional Lie Algebras and Applications in Physics

Preface. 1. Generalities on Lie algebras. 2. Representations of Lie algebras. 3. Nilpotent and solvable Lie algebras. 4. Jordan-Chevalley decomposition. 5. Cartan-Killing form on a Lie algebra. 6. General structure of finite-dimensional complex semisimple Lie algebras. 7. Properties of root spaces. 8. Weyl group of a root system. 9. Classification of finite-dimensional complex semisimple Lie algebras. 10. Kac-Moody algebras and Serre's construction. 11. Gradations of a Lie algebra and center of a Kac-Moody algebra. 12. Generalized Cartan-Killing form. 13. Weyl group and root properties of a Kac-Moody algebra. 14. Classification of Kac-Moody algebras. 15. Real and imaginary roots of Kac-Moody algebras of affine type. 16. Root system of untwisted affine Kac-Moody algebras. 17. Applications in physics - a preview. References. Subject index.

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