The algebraic and geometric classification of nilpotent Leibniz algebras

TL;DR

This paper provides a comprehensive algebraic and geometric classification of complex 5-dimensional nilpotent Leibniz algebras, detailing the structure, components, and rigidity within this algebraic variety.

Contribution

It offers the first complete classification of 5-dimensional nilpotent Leibniz algebras, including the dimension, irreducible components, and rigid algebra identification.

Findings

The variety of these algebras has dimension 24.

There are 10 irreducible components in this variety.

Only one algebra is rigid within the classification.

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent Leibniz algebras. In particular, the variety of complex $5$-dimensional nilpotent Leibniz algebras has dimension $24$ it has $10$ irreducible components (there is only one rigid algebra in this variety).