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Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
 
Front Cover for Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
Available Formats:
Electronic ISBN: 978-1-4704-0084-2
Product Code: MEMO/106/507.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $20.40
Front Cover for Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
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  • Front Cover for Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
  • Back Cover for Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
Available Formats:
Electronic ISBN:  978-1-4704-0084-2
Product Code:  MEMO/106/507.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $20.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1061993; 85 pp
    MSC: Primary 17;

    This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative \({\mathbf Z}_2\)-twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z -operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard \(A^{(1)}_1\)-modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

    Readership

    Mathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. A multi-operator extension of the Jacobi identity
    • 2. A relative twisted Jacobi identity
    • 3. Standard representations of the twisted affine Lie algebra $A^{(1)}_1$
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Volume: 1061993; 85 pp
MSC: Primary 17;

This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative \({\mathbf Z}_2\)-twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z -operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard \(A^{(1)}_1\)-modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

Readership

Mathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory.

  • Chapters
  • Introduction
  • 1. A multi-operator extension of the Jacobi identity
  • 2. A relative twisted Jacobi identity
  • 3. Standard representations of the twisted affine Lie algebra $A^{(1)}_1$
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