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Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The Appendix provides a summary of the basic properties of each Lie algebra of finite and affine type.Read more
- This book, unlike similar titles, includes an account of both the theory of finite dimensional simple Lie Algebras and the more modern theory of Kac-Moody algebras
- The mathematical treatment of the subject is thorough. Proofs are given in detail and the relaxed style makes this a user-friendly title
- Roger Carter is a well known and respected author following the success of his earlier books on group theory and lie theory
Reviews & endorsements
"This monograph provides a crystal clear exposition of the theory of finite-dimensional simple Lie algebras and a nice introduction to (infinite-dimensional) Kac - Moody algebras of affine type. Also, an excellent course on Lie algebras could be constructed starting from the book."
Daniel Beltita, Institute of Mathematics, Romanian Academy, SIAM Review
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- Date Published: December 2005
- format: Hardback
- isbn: 9780521851381
- length: 652 pages
- dimensions: 236 x 159 x 35 mm
- weight: 1.04kg
- contains: 10 b/w illus.
- availability: Available
Table of Contents
1. Basic concepts
2. Representations of soluble and nilpotent Lie algebras
3. Cartan subalgebras
4. The Cartan decomposition
5. The root systems and the Weyl group
6. The Cartan matrix and the Dynkin diagram
7. The existence and uniqueness theorems
8. The simple Lie algebras
9. Some universal constructions
10. Irreducible modules for semisimple Lie algebras
11. Further properties of the universal enveloping algebra
12. Character and dimension formulae
13. Fundamental modules for simple Lie algebras
14. Generalized Cartan matrices and Kac-Moody algebras
15. The classification of generalised Cartan matrices
16 The invariant form, root system and Weyl group
17. Kac-Moody algebras of affine type
18. Realisations of affine Kac-Moody algebras
19. Some representations of symmetrisable Kac-Moody algebras
20. Representations of affine Kac-Moody algebras
21. Borcherds Lie algebras
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