Lie Algebras of Finite and Affine Type
Lie Algebras of Finite and Affine Type
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GBPLie 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 first half of the book deals with classification of the finite dimensional simple Lie algebras and of their finite dimensional irreducible representations. The second half introduces the theory of Kac-Moody algebras, concentrating particularly on those of affine type. A brief account of Borcherds algebras is also included. An Appendix gives 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
Product details
October 2005Adobe eBook Reader
9780511128677
0 pages
0kg
10 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
