| 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 |
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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 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.
ReadershipMathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory.
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Table of Contents
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Chapters
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Introduction
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1. A multi-operator extension of the Jacobi identity
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2. A relative twisted Jacobi identity
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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 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.
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 $A^{(1)}_1$
