Infinite Dimensional Lie Algebras
Published on 24. October 1985
Book
Hardback
298 pages
978-0-521-32133-4 (ISBN)
Description
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.
Reviews / Votes
'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 CanadaMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
10 Tables, unspecified
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 16 mm
Weight
508 gr
ISBN-13
978-0-521-32133-4 (9780521321334)
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Schweitzer Classification
Other editions
New editions
Victor G. Kac
Infinite-Dimensional Lie Algebras
Book
08/1994
3rd Edition
Cambridge University Press
€81.20
Shipment within 15-20 days
Person
Content
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 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. Application to n-function identities. Sugawara operators and branching functions; 13. Affine algebras, theta functions, and modular forms; 14. The principal and homogeneous vertex operator constructions of the basic representation. Boson-Fermion correspondence. Application to soliton equations.