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Introduction to vertex operator algebras and their representations
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Introduction to vertex operator algebras and their representations

Introduction to vertex operator algebras and their representations

James Lepowsky, Haisheng Li - Collection Progress in Mathematics

324 pages, parution le 25/03/2004

Résumé

The deep and relatively new field of vertex operator algebras is intimately related to a variety of areas in mathematics and physics: for example, the concepts of "monstrous moonshine," infinite-dimensional Lie theory, string theory, and conformal field theory. This book introduces the reader to the fundamental theory of vertex operator algebras and its basic techniques and examples. Beginning with detailed presentation of the theoretical foundations and proceeding to a range of applications, the text includes a number of new, original results and also highlights and brings fresh perspective to important works of many researchers.

After introducing the elementary "formal calculus" underlying the subject, the book provides an axiomatic development of vertex operator algebras and their modules, expanding on the early contributions of R. Borcherds, I. Frenkel, J. Lepowsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu and others. The concept of a "representation" of a vertex (operator) algebra is treated in detail, following and extending the work of H. Li; this approach is used to construct important families of vertex (operator) algebras and their modules.

Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The book's self-contained presentation of the core topics will equip readers to embark on many active research directions related to vertex operator algebras, group theory, representation theory, and string theory.

Sommaire

  • Formal calculus
  • Vertex operator algebras: the axiomatic basics
  • Modules
  • Representation of Vertex algebras and the construction Vertex algebras and modules
  • Construction of families of Vertex operator algebras and modules
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) James Lepowsky, Haisheng Li
Collection Progress in Mathematics
Parution 25/03/2004
Nb. de pages 324
Format 15,7 x 24
Couverture Relié
Poids 598g
Intérieur Noir et Blanc
EAN13 9780817634087
ISBN13 978-0-8176-3408-7

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