Lie Algebras of Finite and Affine Type

Roger W. Carter - Collection Cambridge Studies in Advanced Mathematics

632 pages, parution le 08/12/2005

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Résumé

Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra.

The first half of the book deals with classification of the finite dimensional simple Lie algebras and of their finite dimensional irreducible representations.

The second half introduces the theory of Kac-Moody algebras, concentrating particularly on those of affine type. A brief account of Borcherds algebras is also included. An Appendix gives a summary of the basic properties of each Lie algebra of finite and affine type.

This book, unlike similar titles, includes an account of both the theory of finite dimensional simple Lie Algebras and the more modern theory of Kac-Moody algebras

The mathematical treatment of the subject is thorough. Proofs are given in detail and the relaxed style makes this a user-friendly title

Roger Carter is a well known and respected author following the success of his earlier books on group theory and lie theory

Sommaire

Preface
Basic concepts
Representations of soluble and nilpotent Lie algebras
Cartan subalgebras
The Cartan decomposition
The root systems and the Weyl group
The Cartan matrix and the Dynkin diagram
The existence and uniqueness theorems
The simple Lie algebras
Some universal constructions
Irreducible modules for semisimple Lie algebras
Further properties of the universal enveloping algebra
Character and dimension formulae
Fundamental modules for simple Lie algebras
Generalized Cartan matrices and Kac-Moody algebras
The classification of generalised Cartan matrices
The invariant form, root system and Weyl group
Kac-Moody algebras of affine type
Realisations of affine Kac-Moody algebras
Some representations of symmetrisable Kac-Moody algebras
Representations of affine Kac-Moody algebras
Borcherds Lie algebras
Appendix
Notation
Bibliography if books on Lie algebras
Bibliography of articles on Kac-Moody algebras
Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Roger W. Carter
Collection	Cambridge Studies in Advanced Mathematics
Parution	08/12/2005
Nb. de pages	632
Format	15,5 x 23,5
Couverture	Relié
Poids	1160g
Intérieur	Noir et Blanc
EAN13	9780521851381
ISBN13	978-0-521-85138-1