<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Classification of Filiform Lie Algebras up to dimension 7 Over Finite Fields"}

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...

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

Publié en ligne: 21 sept. 2017

Pages: 185 - 204

Reçu: 01 janv. 2015

Accepté: 01 avr. 2015

DOI: https://doi.org/10.1515/auom-2016-0036

Mots clés
Graphs as a tool, classification, filiform Lie algebra, finite fields

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Publié en ligne: 21 sept. 2017

Pages: 185 - 204

Reçu: 01 janv. 2015

Accepté: 01 avr. 2015

DOI: https://doi.org/10.1515/auom-2016-0036

Mots clésGraphs as a tool, classification, filiform Lie algebra, finite fields

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Graphs as a tool, classification, filiform Lie algebra, finite fields