<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

Published Online: Sep 21, 2017

Page range: 185 - 204

Received: Jan 01, 2015

Accepted: Apr 01, 2015

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

Keywords
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

Published Online: Sep 21, 2017

Page range: 185 - 204

Received: Jan 01, 2015

Accepted: Apr 01, 2015

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

KeywordsGraphs as a tool, classification, filiform Lie algebra, finite fields

© 2017

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

Keywords
Graphs as a tool, classification, filiform Lie algebra, finite fields