Introduction to Vertex Operator Algebras and Their Representations: 227 (Progress in Mathematics, 227) - Hardcover

Lepowsky, James; Li, Haisheng

Hardcover

ISBN 10: 0817634088 ISBN 13: 9780817634087

Publisher: Birkhäuser, 2003

Synopsis

The field of vertex operator algebras is an active area of research and plays an integral role in infinite-dimensional Lie theory, string theory, and conformal field theory, and other subdisciplines of mathematics and physics. This book begins with a careful presentation of the theoretical foundations of vertex operator algebras and their modules, and then proceeds to a range of applications. The text features new, original results and a fresh perspective on the important works of many researchers; in particular, it provides a detailed treatment of the concept of a "representation'' of a vertex (operator) algebra. Requiring only a familiarity with basic algebra, this broad, self-contained treatment of the core topics in vertex algebras will appeal to graduate students and researchers in both mathematics and physics.

About this title

Review

"...[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

Synopsis

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 a 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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2003
• Language: English
• ISBN 10: 0817634088
• ISBN 13: 9780817634087
• Binding: Hardcover
• Number of pages: 331