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 $\mathrm{char}(\mathbb{F})\ne 2$. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonné 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.

Conference paper. Final version, accepted for publication

References in corpus (2)

• Two-step nilpotent Leibniz algebras
• Derivations of two-step nilpotent algebras

Cited by in corpus (5)

• Weak representability of actions of non-associative algebras
• Action accessible and weakly action representable varieties of algebras
• Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra
• On Lie-holomorphs of Leibniz algebras
• Derivations in Dialgebras Derivations and Biderivations in Dialgebras