Classification of Filiform Lie Algebras up to dimension 7 Over Finite Fields

This paper tries to develop a recent research which consists in us- ing Discrete Mathematics as a tool in the study of the problem of the classi cation of Lie algebras in general, dealing in this case with liform Lie algebras up to dimension 7 over nite elds. The idea lies in the representation of e...

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Detalles Bibliográficos
Autores: Falcon Ganfornina, Oscar J., Falcon Ganfornina, Raul, Núñez Valdés, Juan, Pacheco Martínez, Ana María, Villar Liñán, María Trinidad
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad Loyola Andalucía
Repositorio:Brújula
OAI Identifier:oai:repositorio.uloyola.es:20.500.12412/2132
Acceso en línea:http://hdl.handle.net/20.500.12412/2132
Access Level:acceso abierto
Palabra clave:Classification
Filiform Lie algebra
Finite fields
Graphs as a tool
Descripción
Sumario:This paper tries to develop a recent research which consists in us- ing Discrete Mathematics as a tool in the study of the problem of the classi cation of Lie algebras in general, dealing in this case with liform Lie algebras up to dimension 7 over nite elds. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we nd out that there exist, up to isomorphism, six, ve and ve 6-dimensional liform Lie algebras and fteen, eleven and fteen 7-dimensional ones, respectively, over Z=pZ, for p = 2; 3; 5. In any case, the main interest of the paper is not the computations itself but both to provide new strategies to nd out properties of Lie algebras and to exemplify a suitable technique to be used in classi cations for larger dimensions.