Geodesic
Directed pseudo-graphs and Lie algebras over finite fields
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 229-239
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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 $\mathbb {Z}/2\mathbb {Z}$. Over $\mathbb {Z}/3\mathbb {Z}$, eight and twenty-two $2$- and $3$-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented.
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 $\mathbb {Z}/2\mathbb {Z}$. Over $\mathbb {Z}/3\mathbb {Z}$, eight and twenty-two $2$- and $3$-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented.
DOI : 10.1007/s10587-014-0096-7
Classification : 05C99, 17B30, 17B45, 17B50, 17B60
Keywords: directed pseudo-graph; adjacency matrix; Lie algebra 
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     title = {Directed pseudo-graphs and {Lie} algebras over finite fields},
     journal = {Czechoslovak Mathematical Journal},
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Boza, Luis; Fedriani, Eugenio Manuel; Núñez, Juan; Pacheco, Ana María; Villar, María Trinidad. Directed pseudo-graphs and Lie algebras over finite fields. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 229-239. doi: 10.1007/s10587-014-0096-7

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