Study of a Family of Lie Algebra over Z/3Z

In this paper, we study and classify a particular family of Lie algebras by using Graph Theory as a tool. The idea lies in the representation of each Lie algebra by a certain graph; then we study the properties of such graphs by using Graph Theory and we translate later these properties to Lie algebras. We apply this procedure to a particular family of Lie algebras over a finite field and we obtain a first classification of them.