On Axiomatic Approaches to Vertex Operator Algebras and Modules (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Frenkel, Igor B.; Huang, Yi-Zhi; Lepowsky, James

Softcover

ISBN 10: 0821825550 ISBN 13: 9780821825556

Publisher: American Mathematical Society, 1993

Synopsis

The notion of vertex operator algebra arises naturally in the vertex operator construction of the Monster - the largest sporadic finite simple group. From another perspective, the theory of vertex operator algebras and their modules forms the algebraic foundation of conformal field theory. Vertex operator algebras and conformal field theory are now known to be deeply related to many important areas of mathematics. This essentially self-contained monograph develops the basic axiomatic theory of vertex operator algebras and their modules and intertwining operators, following a fundamental analogy with Lie algebra theory. The main axiom, the 'Jacobi(-Cauchy) identity', is a far-reaching analog of the Jacobi identity for Lie algebras.The authors show that the Jacobi identity is equivalent to suitably formulated rationality, commutativity, and associativity properties of products of quantum fields. A number of other foundational and useful results are also developed. This work was originally distributed as a preprint in 1989, and in view of the current widespread interest in the subject among mathematicians and theoretical physicists, its publication and availability should prove no less useful than when it was written.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 0821825550
• ISBN 13: 9780821825556
• Binding: Paperback
• Number of pages: 64