On Metric Leibniz Algebras and Deformations

TL;DR

This paper classifies low-dimensional metric Leibniz algebras over complex numbers up to five dimensions, analyzing their deformations and providing explicit formulas for cocycles and metric deformations.

Contribution

It offers a detailed classification and explicit deformation formulas for low-dimensional metric Leibniz algebras, highlighting metric deformations.

Findings

Explicit formulas for cocycles and deformations

Classification of metric Leibniz algebras up to five dimensions

Identification of metric deformations among all deformations

Abstract

In this note we consider low dimensional metric Leibniz algebras with an invariant inner product over the complex numbers up to five dimension. We study their deformations, and give explicit formulas for the cocycles and deformations. We identify among those the metric deformations.