Series: Studies in Mathematical Physics

This series aims at discussing recent developments in physics offering sound mathematics and a high didactical qualtiy. The emphasis lies on techniques, ideas and methods that are fundamental, interesting and innovating in both mathematics and physics, herewith building a bridge between the two disciplines.
Book Series: Lie Algebras, Part 2

Most recent volume

Volume 7. Lie Algebras, Part 2

Published: 30th October 1997 Authors: E.A. de Kerf G.G.A. Bäuerle A.P.E. ten Kroode
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.

Additional volumes

Volume 2. Structures in Dynamics

Published: 5th November 1991 Authors: H.W. Broer F. Dumortier S.J. van Strien F. Takens