Lie Algebras of Finite and Affine Type
Lie Algebras of Finite and Affine Type
$139.00
USDLie 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.
- 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
Product details
December 2005Hardback
9780521851381
652 pages
236 × 159 × 35 mm
1.04kg
10 b/w illus.
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
- Appendix.
