Electronic ISBN:  9781470400842 
Product Code:  MEMO/106/507.E 
List Price:  $34.00 
MAA Member Price:  $30.60 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 106; 1993; 85 ppMSC: Primary 17;
This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multioperator 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 Zoperator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The LepowskyWilson generating function identities correspond to the identities involved in the construction of a basis for the space of Cdisorder fields of such parafermion algebras.
ReadershipMathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory.

Table of Contents

Chapters

Introduction

1. A multioperator 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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This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multioperator 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 Zoperator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The LepowskyWilson generating function identities correspond to the identities involved in the construction of a basis for the space of Cdisorder fields of such parafermion algebras.
Mathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory.

Chapters

Introduction

1. A multioperator extension of the Jacobi identity

2. A relative twisted Jacobi identity

3. Standard representations of the twisted affine Lie algebra $A^{(1)}_1$