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arXiv · 2209.07892

Biderivations of low-dimensional Leibniz algebras

Manuel Mancini
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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.

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Manuel Mancini. 2022-09-16. Biderivations of low-dimensional Leibniz algebras. https://doi.org/10.1007/978-3-031-32707-0_8

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