Principal construction of the toroidal Lie algebra of type \(A_1\)
type: Item
instance of: scholarly article
title: Principal construction of the toroidal Lie algebra of type \(A_1\)
zbMATH Open document ID: 0932.17028
DOI: 10.1007/PL00004710
author: Shaobin Tan
published in: Mathematische Zeitschrift
publication date: 2000-03-12T00:00:00Z
review text: A toroidal Lie algebra is a perfect central extension of the Lie algebra \({\mathcal G}\otimes A_\nu\) where \({\mathcal G}\) is a finite-dimensional simple Lie algebra, and \(A_\nu\) is the ring of Laurent polynomials in commuting variables. In this paper we consider an analogue of the level one principal representation of the affine Kac-Moody algebra \(A_1^{(1)}\) by vertex operators to the toroidal case. We construct a module for the toroidal Lie algebra and an extended toroidal algebra of type \(A_1\). The Fock module representation obtained here is faithful and completely reducible over the extended toroidal Lie algebra. Some structure of the module is also studied in the paper.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 1336851
zbMATH Keywords: toroidal Lie algebra
zbMATH Keywords: level one principal representation
zbMATH Keywords: affine Kac-Moody algebra
zbMATH Keywords: vertex operators
zbMATH Keywords: Fock module
Wikidata QID: Q115390564
reviewed by: Ser Peow Tan
MaRDI profile type: Publication
full work available at URL: pl00004710
OpenAlex ID: W1990178551
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description: scientific article; zbMATH DE number 1336851