Computational Methods for Biderivations of 4-dimensional nilpotent complex leibniz algebras

TL;DR

This paper develops algorithms and uses computer algebra software to compute biderivations of 4-dimensional nilpotent complex Leibniz algebras, providing detailed descriptions and examples based on their classification.

Contribution

It introduces computational methods and algorithms for determining biderivations of these algebras, leveraging existing classifications and software tools.

Findings

Algorithms for computing derivations, antiderivations, and biderivations

Explicit matrix representations of biderivations

Illustrative examples demonstrating the computational approach

Abstract

This paper focuses on the biderivations of 4-dimensional nilpotent complex Leibniz algebras. Using the existing classification of these algebras, we develop algorithms to compute derivations, antiderivations, and biderivations as pairs of matrices with respect to a fixed basis. By utilizing computer algebra software such as Mathematica and Maple, we provide detailed descriptions and examples to illustrate these computations.