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.
Lie Algebras, Part 2

Most recent volume

Volume 7. Lie Algebras, Part 2

Published: 30th October 1997 Editors: E.A. de Kerf A.P.E. ten Kroode G.G.A. Bäuerle
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 6. Mathematical Structures in Continuous Dynamical Systems

Published: 23rd February 1995 Editors: E. van Groesen E.M. de Jager

Volume 5. The Mathematical Foundations of Gauge Theories

Published: 18th June 1992 Editors: K.B. Marathe G. Martucci

Volume 4. Green Functions for Ordered and Disordered Systems

Published: 25th March 1992 Editors: A. Gonis

Volume 3. Huygens' Principle 1690 - 1990: Theory and Applications

Published: 6th February 1992 Editors: H.A. Ferwerda H. Blok H.K. Kuiken

Volume 2. Structures in Dynamics

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

Volume 1. Lie Algebras, Part 1

Published: 14th December 1990 Editors: E.A. de Kerf G.G.A. Bäuerle