Lie Algebras Pt. 2 : Finite and Infinite Dimensional Lie Algebras and Applications in Physics

by De Kerf, E. A.; Bauerle, G. G. A.; Kerf, E. A. De; Kroode, A. P. E. Ten

• ISBN13: 9780444828361
• ISBN10: 0444828362
• Format: Hardcover
• Copyright: 1997-05-01
• Publisher: Elsevier Science Serials

Summary

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.

Table of Contents

Preface

Extensions of Lie algebras

Explicit construction of affine Kac-Moody algebras

Representations - enveloping algebra techniques

The Weyl group and integrable representations

More on representations

Characters and multiplicities

Quarks, leptons and gauge fields

Lie algebras of infinite matrices

Representations of loop algebras

KP-hierarchies

Conformal symmetry

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