Boza, Luis , Manuel Fedriani, Eugenio , Nunez, Juan , PACHECO MARTÍNEZ, ANA MARÍA, Trinidad Villar, Maria
No
Czech. Math. J.
Article
Científica
0.288
0.413
01/03/2014
000340548200020
2-s2.0-84906047110
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 a"currency sign/2a"currency sign. Over a"currency sign/3a"currency sign, eight and twenty-two 2- and 3-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented.
directed pseudo-graph; adjacency matrix; Lie algebra