+612 9045 4394
Affine Lie Algebras and Quantum Groups : An Introduction, with Applications in Conformal Field Theory - Jurgen A. Fuchs

Affine Lie Algebras and Quantum Groups

An Introduction, with Applications in Conformal Field Theory

By: Jurgen A. Fuchs, P. V. Landshoff (Editor), David R. Nelson (Editor), S. Weinberg (Editor)

Paperback Published: 8th May 1995
ISBN: 9780521484121
Number Of Pages: 448

Share This Book:


RRP $112.95
or 4 easy payments of $23.20 with Learn more
Ships in 10 to 15 business days

This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.

Industry Reviews

'I can recommend it unreservedly as an introduction, but also as a review for experts.' Physikalishe Blatter '... a very valuable book ... of interest to mathematicians and physicists working in the areas of conformal field theory, representation theory of infinite-dimensional Lie algebras and vertex operator algebras.' Drazen Adomovic, Zentralblatt fur Mathematik

Prefacep. xi
Semisimple Lie algebrasp. 1
Basic conceptsp. 2
Representations and modulesp. 11
The Killing form. Real and complex Lie algebrasp. 19
The Cartan-Weyl basisp. 23
Classification of simple Lie algebrasp. 38
Highest weight modulesp. 49
The Weyl group. Charactersp. 70
Branching rulesp. 81
Literaturep. 87
Affine Lie algebrasp. 89
Classification of Kac-Moody algebrasp. 90
Loop algebras and central extensionsp. 100
The root systemp. 108
Highest weight modulesp. 116
Null vectorsp. 125
The Weyl group. Charactersp. 130
Modular transformationsp. 137
Branching rulesp. 143
Literaturep. 147
WZW theoriesp. 149
Operator productsp. 150
The Sugawara constructionp. 159
Conformal field theoryp. 167
The Knizhnik-Zamolodchikov equationp. 179
The Gepner-Witten equationp. 192
Free fermionsp. 203
Quantum equivalencep. 214
Conformal embeddingsp. 226
Literaturep. 238
Quantum groupsp. 242
Hopf algebrasp. 243
Deformations of enveloping algebrasp. 257
Representation theoryp. 267
Quantum dimensionsp. 278
The truncated Kronecker productp. 289
R-matricesp. 297
Quantized groupsp. 305
Affine Lie algebras and quantum groupsp. 313
Literaturep. 319
Duality, fusion rules, and modular invariancep. 322
Fusion rule algebrasp. 323
Modular invariancep. 331
Fusion rules and modular transformationsp. 339
Modular invariantsp. 347
WZW fusion rules and truncated tensor productsp. 354
Chiral blocksp. 367
Fusing and braidingp. 373
Screened vertex operators and quantum groupsp. 384
Literaturep. 402
Referencesp. 405
Indexp. 428
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521484121
ISBN-10: 052148412X
Series: Cambridge Monographs on Mathematical Physics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 448
Published: 8th May 1995
Country of Publication: GB
Dimensions (cm): 23.67 x 19.05  x 2.39
Weight (kg): 0.76