Classification of 5-Dimensional Complex Nilpotent Leibniz Algebras

2017/06/03 by Demir, Ismail
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1706.00951

Abstract

Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of 5-dimensional complex non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms to classify the case dim(A²)=3 and dim(Leib(A))=1 which can be applied to higher dimensions. The remaining cases are classified via direct method.

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