An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
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: $20.40 Click above image for expanded view Extensions of the Jacobi Identity for Vertex Operators, and Standard$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.

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 $A^{(1)}_1$
• Request Review Copy
• Get Permissions
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.

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