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...
| Authors: | , , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41616 |
| Online Access: | http://hdl.handle.net/11441/41616 https://doi.org/10.1007/s10587-014-0096-7 |
| Access Level: | Open access |
| Keyword: | directed pseudo-graph adjacency matrix Lie algebra |
| Summary: | 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 2-and 3-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented. |
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