Extensions of the Jacobi identity for generalized vertex algebras
type: Item
instance of: scholarly article
title: Extensions of the Jacobi identity for generalized vertex algebras
zbMATH Open document ID: 0844.17021
DOI: 10.1016/0022-4049(95)00011-9
author: Cristiano Husu
published in: Journal of Pure and Applied Algebra
publication date: 1996-09-03T00:00:00Z
review text: The Jacobi identity for vertex algebras relates compositions of vertex operators \(Y(Y(u, z_0) v,z_2)\), say \(Y_2 \circ Y_0\) for short, with products of vertex operators such as \(Y(u, z_1) Y(v, z_2)\), say \(Y_1 \cdot Y_2\) for short. In [Mem. Am. Math. Soc. 507 (1993; Zbl 0798.17013)] the author has extended the Jacobi identity for vertex algebras to multi-operator identities for expressions of the form \(Y_1 \circ \cdots \circ Y_m \circ (Y_{m + 1} \cdot \dots \cdot Y_n)\). In the paper under review this result is extended further for generalized vertex algebras [cf. \textit{C. Dong} and \textit{J. Lepowsky}, Generalized vertex algebras and relative vertex operators, Prog. Math. 112, Birkhäuser, Boston (1993; Zbl 0803.17009)]. This work is motivated by vertex operator constructions of representations of affine Lie algebras and the corresponding \(Z\)-algebras [cf. \textit{C. Husu}, J. Pure Appl. Algebra 98, 163-187 (1995; Zbl 0837.17013)].
reviewed by: Mirko Primc
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 858638
zbMATH Keywords: vertex algebras
zbMATH Keywords: vertex operators
zbMATH Keywords: multi-operator identities
zbMATH Keywords: generalized vertex algebras
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00011-9
OpenAlex ID: W2125945495
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description: scientific article; zbMATH DE number 858638