Extensions of the Jacobi identity for vertex operators, and standard A[1][(1)]-modules
Author(s)
Bibliographic Information
Extensions of the Jacobi identity for vertex operators, and standard A[1][(1)]-modules
（Memoirs of the American Mathematical Society, no. 507）
American Mathematical Society, 1993
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Note
"November 1993, volume 106, number 507 (second of 6 numbers)"--T.p
Rev. version of the author's thesis (doctoral)--Rutgers University
Includes bibliographical references (p. 84-85)
Description and Table of Contents
Description
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.
Table of Contents
Introduction A multi-operator extension of the Jacobi identity A relative twisted Jacobi identity Standard representations of the twisted affine Lie algebra $A^{(1)}_1$ References.
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