A geometric presentation for the adjoint module of \(SL_ 3(k)\)
type: Item
instance of: scholarly article
title: A geometric presentation for the adjoint module of \(SL_ 3(k)\)
zbMATH Open document ID: 0688.20021
DOI: 10.1016/0021-8693(89)90278-0
author: Stephen D. Smith
author: Helmut Völklein
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let k be a field and A the adjoint \(SL_ 3(k)\)-module arising from the adjoint action of \(SL_ 3(k)\) on \(3\times 3\) matrices with zero traces. The authors give a geometrical characterization of A in terms of the geometry of the projective plane \(Pk^ 3\). This paper is a part of the more general program of characterizing modules by means of subspaces determined by the geometry. Other works of this program are \textit{M. A. Ronan} and \textit{S. D. Smith} [J. Algebra 96, 319-346 (1985; Zbl 0604.20043), Commun. Algebra 17, 1199-1237 (1989; Zbl 0676.20007), J. Algebra 102, 135-154 (1986; Zbl 0602.20014)].
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 51E25
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4127498
zbMATH Keywords: geometry of group representations
zbMATH Keywords: \(SL_ 3(k)\)-module
zbMATH Keywords: adjoint action
zbMATH Keywords: projective plane
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90278-0
OpenAlex ID: W1987420572
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description: scientific article; zbMATH DE number 4127498