Lie Algebras of Finite and Affine Type / Edition 1

by Roger Carter

Overview

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.

Product Details

ISBN-13:	9780521851381
Publisher:	Cambridge University Press
Publication date:	10/27/2005
Series:	Cambridge Studies in Advanced Mathematics , #96
Edition description:	New Edition
Pages:	652
Product dimensions:	6.26(w) x 9.29(h) x 1.38(d)

About the Author

Roger Carter is an Emeritus Professor of Mathematics at the University of Warwick.

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.

Editorial Reviews

"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

From the Publisher