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© 2004

Introduction to Vertex Operator Algebras and Their Representations

Textbook

Part of the Progress in Mathematics book series (PM, volume 227)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. James Lepowsky, Haisheng Li
    Pages 1-19
  3. James Lepowsky, Haisheng Li
    Pages 21-48
  4. James Lepowsky, Haisheng Li
    Pages 49-116
  5. James Lepowsky, Haisheng Li
    Pages 117-143
  6. James Lepowsky, Haisheng Li
    Pages 191-287
  7. Back Matter
    Pages 289-321

About this book

Keywords

Group theory Lattice Representation theory algebra ring theory

Authors and affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA
  2. 2.Department of MathematicsRutgers UniversityCamdenUSA

Bibliographic information

Reviews

"…[The] authors give a systematic introduction to the theory of vertex operator algebras and their representations. Particular emphasis is put on the axiomatic development of the theory and the construction theorems for vertex operator algebras and their modules. The book provides a detailed study of most basic families of vertex operator algebras and their representation theory. A number of new, original results are presented…. This excellent book is written in a self-contained manner with detailed proofs. It will be useful for graduate students and active researchers interested in the theory of vertex operator algebras and their applications."

—Mathematical Reviews

"The book under review treats modules for vertex operator algebras and, more importantly, it gives an answer to the following important questions:"How do we construct modules for VOAs?" The answer to this question is the essense of this new exciting book. . . The book is written with care, clarity and pateience which is typical for both authros.  It is self-contained with no details omitted.  Misprints are most probably rare (if any). Even an advanced undergraduate can pick up a book and learn a whole new exciting subject. In my opinion this beautiful book has only one shortcoming - the list of references (around 600 items!). The authors were kind enough to give credit to almost everyone who ever contributed in some way to vertex operator algebra theory."  ---Zentralblatt

"The book gives a sound introduction in the theory of vertex algebras emphasizing in particular the construction of families of examples by means of a kind of representations developped by the second named author."

---Monatsheft für Mathematik