On Classification of Four Dimensional Nilpotent Leibniz Algebras

TL;DR

This paper classifies four-dimensional non-Lie nilpotent Leibniz algebras using canonical forms and matrix techniques, expanding understanding of algebraic structures beyond Lie algebras.

Contribution

It provides the first complete classification of four-dimensional non-Lie nilpotent Leibniz algebras, employing novel matrix and congruence class methods.

Findings

Complete classification of four-dimensional non-Lie nilpotent Leibniz algebras

Use of canonical forms for matrix congruence classes

Application of bilinear form techniques

Abstract

Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of four dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.