Lie Algebras: Finite and Infinite Dimensional Lie Algebras and Applications in Physics

E.A. De Kerf, G.G.A. Bäuerle and A.P.E. Ten Kroode (Eds.)9780444828361, 0444828362

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

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Table of contents :
Content:
Preface from the editors
Pages vii-x
E.M. de Jager

Chapter 18 Extensions of Lie algebras Original Research Article
Pages 5-48

Chapter 19 Explicit construction of affine Kac-Moody algebras Original Research Article
Pages 49-70

Chapter 20 Representations—enveloping algebra techniques Original Research Article
Pages 71-113

Chapter 21 The Weyl group and integrable representations Original Research Article
Pages 115-156

Chapter 22 More on representations Original Research Article
Pages 157-217

Chapter 23 Characters and multiplicities Original Research Article
Pages 219-258

Chapter 24 Quarks, leptons and gauge fields Original Research Article
Pages 259-304

Chapter 25 Lie algebras of infinite matrices Original Research Article
Pages 305-364

Chapter 26 Representations of loop algebras Original Research Article
Pages 365-429

Chapter 27 KP-hierarchies Original Research Article
Pages 431-476

Chapter 28 Conformal symmetry Original Research Article
Pages 477-541

Bibliography
Pages 543-549

Index
Pages 550-554