On an explicit isomorphism of standard level-one modules for \(\hat D_{4n}\)
type: Item
instance of: scholarly article
title: On an explicit isomorphism of standard level-one modules for \(\hat D_{4n}\)
zbMATH Open document ID: 0876.17023
author: Julie Glass
published in: Journal of Algebra
publication date: 1997-11-13T00:00:00Z
review text: This paper forms part of the program of finding alternative constructions of the Monster simple group. The affine Kac-Moody algebra of type \(\hat D_{4n} \) has four non-isomorphic irreducible highest-weight modules of level 1. Using vertex operator techniques, the idea of the paper is to construct a set of twisted forms of the algebra and give an explicit description of the four irreducible modules for each algebra. The author gives isomorphisms between the algebras and explicit graded isomorphisms between the matching pairs of modules. Using this explicit isomorphism, one may then give a \(Z_6\)-orbifold construction of the Monster for the affine algebra associated to a direct sum of six copies of \(D_{4}\).
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 1013983
zbMATH Keywords: irreducible modules
zbMATH Keywords: vertex operators
zbMATH Keywords: Monster simple group
zbMATH Keywords: Kac-Moody algebras
zbMATH Keywords: orbifold construction
reviewed by: Duncan J. Melville
MaRDI profile type: Publication
full work available at URL: jabr.1996.6875
OpenAlex ID: W2020378321
cites work: Vertex algebras, Kac-Moody algebras, and the Monster
cites work: Finite subgroups of G2,(c)
cites work: Integral Cayley numbers
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cites work: Introduction to Lie Algebras and Representation Theory
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cites work: Calculus of twisted vertex operators
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cites work: Q4146925
DOI: 10.1006/JABR.1996.6875
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description: scientific article; zbMATH DE number 1013983