Lie Algebras, Part 2: Finite and Infinite Dimensional Lie Algebras and Applications in Physics

E. A. de Kerf

ISBN 10: 0444542329 / ISBN 13: 9780444542328

Published by North Holland, 2011

About this Item

568 pages. 8.74x5.83x1.57 inches. In Stock.

Seller Inventory # zk0444542329

Bibliographic Details

• Title: Lie Algebras, Part 2: Finite and Infinite Dimensional Lie Algebras and Applications in Physics
• Publisher: North Holland
• Publication Date: 2011
• Language: English
• ISBN 10: 0444542329
• ISBN 13: 9780444542328
• Binding: Paperback
• Condition: Brand New

About this title

Synopsis

This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.