Biderivations of low-dimensional Leibniz algebras

Abstract

In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field $\mathbb{F}$, with $\operatorname{char}(\mathbb{F})\neq 2$. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonn\'e Leibniz algebra $\mathfrak{d}_1$. Eventually we give an algorithm for finding derivations and anti-derivations of a Leibniz algebra as pair of matrices with respect to a fixed basis.