Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
type: Item
instance of: scholarly article
title: Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
zbMATH Open document ID: 0808.17018
DOI: 10.1007/BF02102638
author: Robert V. Moody
author: S. Eswara Rao
published in: Communications in Mathematical Physics
publication date: 1994-03-23T00:00:00Z
review text: We construct faithful vertex operator representations for the universal central extension \(\tau_ n\) of \({\mathfrak g}\otimes \mathbb{C}[ t_ 1^{\pm1}, t_ 2^{\pm1}, \dots, t_ n^{\pm1} ]\), where \({\mathfrak g}\) is a simple, simply-laced finite dimensional Lie algebra over \(\mathbb{C}\). We call \(\tau_ n\) the \(n\)-toroidal Lie algebra. These representations also afford representations for an abelian extension of the Lie algebra of derivations of \(\mathbb{C}[ t_ 1^{\pm1}, t_ 2^{\pm1}, \dots, t_ n^{\pm1} ]\). This latter Lie algebra is a generalization of the Virasoro algebra, and so this whole construction is a generalization of both the Frenkel-Kac and the Segal-Sugawara construction which are well known for the case \(n=1\).
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 509906
zbMATH Keywords: toroidal Lie algebra
zbMATH Keywords: vertex operator representations
zbMATH Keywords: universal central extension
zbMATH Keywords: Virasoro algebra
MaRDI profile type: Publication
Wikidata QID: Q115392791
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full work available at URL: https://doi.org/10.1007/bf02102638
OpenAlex ID: W2048883261
description: scientific article; zbMATH DE number 509906