# Classification of $5$-Dimensional Complex Nilpotent Leibniz Algebras

## TL;DR

This paper classifies 5-dimensional complex non-Lie nilpotent Leibniz algebras, using canonical forms and direct methods, providing a comprehensive understanding of their structure.

## Contribution

It offers the first complete classification of 5-dimensional complex non-Lie nilpotent Leibniz algebras, employing canonical forms for certain cases and direct methods for others.

## Key findings

- Classification of all 5-dimensional complex non-Lie nilpotent Leibniz algebras
- Use of canonical forms for matrices of bilinear forms in classification
- Application of direct methods for remaining cases

## 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.

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Source: https://tomesphere.com/paper/1706.00951