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Directed pseudo-graphs and Lie algebras over finite fields

Luis B. BozaEugenio Manuel FedrianiJuan NúñezAna María PachecoMaría Trinidad Villar — 2014

Czechoslovak Mathematical Journal

The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudo-graph. As partial results, it is deduced that there exist, up to isomorphism, four, six, fourteen and thirty-four 2 -, 3 -, 4 -, and 5 -dimensional algebras of the studied family, respectively, over the field / 2 . Over / 3 , eight and twenty-two 2 - and 3 -dimensional Lie algebras, respectively, are also found. Finally,...

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