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Directed pseudo-graphs and Lie algebras over finite fields

 

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Author: Boza Prieto, Luis
Fedriani Martel, Eugenio Manuel
Núñez Valdés, Juan
Pacheco Martínez, Ana María
Villar Liñán, María Trinidad
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2014-03
Published in: Czechoslovak Mathematical Journal, 64 (1), 229-239.
Document type: Article
Abstract: 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 Z/2Z. Over Z/3Z, eight and twenty-two 2-and 3-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented.
Cite: Boza Prieto, L., Fedriani Martel, E.M., Núñez Valdés, J., Pacheco Martínez, A.M. y Villar Liñán, M.T. (2014). Directed pseudo-graphs and Lie algebras over finite fields. Czechoslovak Mathematical Journal, 64 (1), 229-239.
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URI: http://hdl.handle.net/11441/41616

DOI: http://dx.doi.org/10.1007/s10587-014-0096-7

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