Infinite-Dimensional Lie Algebras
This 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.
- Electronic book text
- 11 May 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 3rd Revised edition
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.
'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