Extensions Of The Jacobi Identity For Vertex Operators And Standard A Modules
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Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
Author: Cristiano Husu
language: en
Publisher: American Mathematical Soc.
Release Date: 1993
The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z2-twisted vertex operators are introduced and a Jacobi identity for these operators is established. Then these ideas are used to interpret and recover the twisted [bold capital]Z-operators and corresponding generating function identities developed by Lepowsky and R. L. Wilson. This work is closely related to the twisted parafermion algebra constructed by Zamolodchikov-Fateev.
Extensions of the Jacobi Identity for Vertex Operators and Standard A]-Modules
Author: Cristiano Husu
language: en
Publisher: American Mathematical Society(RI)
Release Date: 2014-08-31
This work extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative 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.
Introduction to Vertex Operator Algebras and Their Representations
Author: James Lepowsky
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.