Lie Algebras, Part 2

Finite and Infinite Dimensional Lie Algebras and Applications in Physics

E.A. de Kerf, G.G.A. Bäuerle, A.P.E. ten Kroode

• Publisher: North Holland
• Year: 1997
• Print ISBN:
  9780444828361
• eBook ISBN:
  9780080535463
• Topic: Physical Sciences
• Subtopic: Algebra

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

• Front Cover
• Finite and Infinite Dimensional Lie Algebras and Applications in Physics
• Copyright Page
• Contents
• Chapter 18. Extensions of Lie algebras
• Chapter 19. Explicit construction of affine Kac–Moody algebras
• Chapter 20. Representations—nenveloping algebr a techniques
• Chapter 21. The Weyl group and integrable representations
• Chapter 22. More on representations
• Chapter 23. Characters and multiplicities
• Chapter 24. Quarks, leptons and gauge fields
• Chapter 25. Lie algebras of infinite matrices
• Chapter 26. Representations of loop algebras
• Chapter 27. KP-hierarchies
• Chapter 28. Conformal symmetry
• Bibliography
• Index