Infinite-Dimensional Lie Algebras
Infinite-Dimensional Lie Algebras
$71.99
USDThis is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.
- Highly acclaimed in its hardback edition
- Of interest to mathematical physicists as well as algebraists
- Kac is one of the best-known names in this field; he is one of the founders of the subject
Reviews & endorsements
'A clear account of Kac–Moody algebras by one of the founders … Eminently suitable as an introduction … with a surprising number of exercises.' American Mathematical Monthly
' … a useful contribution. All the basic elements of the subject are covered … Many results which were previously scattered about in the literature are collected here … The book also contains many exercises and useful comments …' Physics in Canada
Product details
August 1994Paperback
9780521466936
424 pages
229 × 152 × 24 mm
0.62kg
Available
Table of Contents
- Introduction
- Notational conventions
- 1. Basic definitions
- 2. The invariant bilinear form and the generalized casimir operator
- 3. Integrable representations of Kac-Moody algebras and the weyl group
- 4. A classification of generalized cartan matrices
- 5. Real and imaginary roots
- 6. Affine algebras: the normalized cartan invariant form, the root system, and the weyl group
- 7. Affine algebras as central extensions of loop algebras
- 8. Twisted affine algebras and finite order automorphisms
- 9. Highest-weight modules over Kac-Moody algebras
- 10. Integrable highest-weight modules: the character formula
- 11. Integrable highest-weight modules: the weight system and the unitarizability
- 12. Integrable highest-weight modules over affine algebras
- 13. Affine algebras, theta functions, and modular forms
- 14. The principal and homogeneous vertex operator constructions of the basic representation
- Index of notations and definitions
- References
- Conference proceedings and collections of paper.
