Classification of 4-dimensional nilpotent complex Leibniz algebras

TL;DR

This paper extends the classification of nilpotent complex Leibniz algebras from dimensions less than 3 to dimension four, providing a comprehensive categorization of these algebraic structures.

Contribution

It offers the first complete classification of 4-dimensional nilpotent complex Leibniz algebras, building upon prior low-dimensional classifications.

Findings

Classification of 4-dimensional nilpotent Leibniz algebras completed

Identification of new algebraic structures in dimension four

Extension of previous low-dimensional results

Abstract

The Leibniz algebras appeared as a generalization of the Lie algebras. In this work we deal with the classification of nilpotent complex Leibniz algebras of low dimensions. Namely, the classification of nilpotent complex Leibniz algebras dimensions less than 3 is extended to the dimension four. {\it AMS Subject Classifications}: 16D70, 17A30, 17A60, 17B30 {\it Key words:} Leibniz algebra, associative algebra, nilpotence, nulfiliform Leibniz algebra, filiform Leibniz algebra.