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Classification of filiform Lie algebras up to dimension 7 over finite fields

 

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Opened Access Classification of filiform Lie algebras up to dimension 7 over finite fields
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Author: Falcón Ganfornina, Óscar Jesús
Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
Pacheco Martínez, Ana María
Villar Liñán, María Trinidad
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2016
Published in: Analele Stiintifice ale Universitatii Ovidius Constanta : Seria Matematica, 24 (2), 185-204.
Document type: Article
Abstract: This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie algebras up to dimension 7 over finite fields. 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 find out that there exist, up to isomorphism, six, five and five 6-dimensional filiform Lie algebras and fifteen, eleven and fifteen 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 find out properties of Lie algebras and to exemplify a suitable technique to be used in classifications for larger dimensions.
Cite: Falcón Ganfornina, Ó.J., Falcón Ganfornina, R.M., Núñez Valdés, J., Pacheco Martínez, A.M. y Villar Liñán, M.T. (2016). Classification of filiform Lie algebras up to dimension 7 over finite fields. Analele Stiintifice ale Universitatii Ovidius Constanta : Seria Matematica, 24 (2), 185-204.
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URI: http://hdl.handle.net/11441/45213

DOI: 10.1515/auom-2016-0036

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