Classification of $5$-Dimensional Complex Nilpotent Leibniz Algebras

Ismail Demir

Classification of $5$-Dimensional Complex Nilpotent Leibniz Algebras

Rings and Algebras 2017-06-06 v1

Authors: Ismail Demir

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 $\dim(A^2)=3$ and $\dim(Leib(A))=1$ which can be applied to higher dimensions. The remaining cases are classified via direct method.

Keywords

lie algebras and superalgebras algebra classification and gradings lie algebras

Cite

@article{arxiv.1706.00951,
  title  = {Classification of $5$-Dimensional Complex Nilpotent Leibniz Algebras},
  author = {Ismail Demir},
  journal= {arXiv preprint arXiv:1706.00951},
  year   = {2017}
}

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