Local systems of vertex operators, vertex superalgebras and modules
type: Item
instance of: scholarly article
title: Local systems of vertex operators, vertex superalgebras and modules
zbMATH Open document ID: 0854.17035
DOI: 10.1016/0022-4049(95)00079-8
author: Haisheng Li
published in: Journal of Pure and Applied Algebra
publication date: 1996-07-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9406185
review text: For an associative algebra \(A\), the representation of \(A\) on a vector space \(M\) is given by an algebra homomorphism from \(A\) to \(\text{End}\,M\). Vertex operator algebras are natural one-variable analogues of commutative associative algebras with an identity element. The author introduces so-called ``local systems of vertex operator algebras'', which are analogues of \(\text{End}\,M\). These local systems form vertex algebras, whose axioms can be obtained from those of vertex operator algebras by dropping the Virasoro relation. Then the representation of a vertex operator algebra \(V\) on a vector space \(M\) is given by a vertex algebra homomorphism from \(V\) to a local system over \(M\).
reviewed by: Xiaoping Xu
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 896554
zbMATH Keywords: modules
zbMATH Keywords: Jacobi identity
zbMATH Keywords: commutativity
zbMATH Keywords: local systems
zbMATH Keywords: representation
zbMATH Keywords: vertex operator algebra
zbMATH Keywords: vertex algebra homomorphism
MaRDI profile type: Publication
OpenAlex ID: W2069086263
arXiv ID: hep-th/9406185
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description: scientific article