Directed pseudo-graphs and lie algebras over finite fields

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 thirt...

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Detalles Bibliográficos
Autores: Boza, Luis, Fedriani, Eugenio Manuel, Núñez-Cortes Contreras, Pilar, Pacheco Martínez, Ana María, Villar Liñán, María Trinidad
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Loyola Andalucía
Repositorio:Brújula
OAI Identifier:oai:repositorio.uloyola.es:20.500.12412/1121
Acceso en línea:http://hdl.handle.net/20.500.12412/1121
Access Level:acceso abierto
Palabra clave:Directed pseudo-graph
Adjacency matrix
Lie algebra
Descripción
Sumario: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 2and 3-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented