Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
On Axiomatic Approaches to Vertex Operator Algebras and Modules
 
On Axiomatic Approaches to Vertex Operator Algebras and Modules
eBook ISBN:  978-1-4704-0071-2
Product Code:  MEMO/104/494.E
List Price: $31.00
MAA Member Price: $27.90
AMS Member Price: $18.60
On Axiomatic Approaches to Vertex Operator Algebras and Modules
Click above image for expanded view
On Axiomatic Approaches to Vertex Operator Algebras and Modules
eBook ISBN:  978-1-4704-0071-2
Product Code:  MEMO/104/494.E
List Price: $31.00
MAA Member Price: $27.90
AMS Member Price: $18.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1041993; 64 pp
    MSC: Primary 17; 81

    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.

    Readership

    Professional mathematicians and graduate students working in algebra, representation theory, and finite groups.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Vertex operator algebras
    • 3. Duality for vertex operator algebras
    • 4. Modules
    • 5. Duality for modules
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1041993; 64 pp
MSC: Primary 17; 81

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.

Readership

Professional mathematicians and graduate students working in algebra, representation theory, and finite groups.

  • Chapters
  • 1. Introduction
  • 2. Vertex operator algebras
  • 3. Duality for vertex operator algebras
  • 4. Modules
  • 5. Duality for modules
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.