Low-dimensional filiform lie algebras over finite fields

Oscar J. Falcón,Juan Núñez,Ana M. Pacheco,M. Trinidad Villar

ICACM'11: Proceedings of the 2011 international conference on Applied & computational mathematics（2011）

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摘要

In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras 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 results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/ p Z, for p = 2; 3; 5.

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关键词

Graph Theory,6-dimensional filiform Lie algebra,Lie algebra,low-dimensional filiform Lie algebra,certain type,finite field,Low-dimensional filiform lie algebra

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