A geometric presentation for the adjoint module of \(SL_ 3(k)\)
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)].
scientific article; zbMATH DE number 4127498
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