论文标题
低维莱布尼兹代数的竞标
Biderivations of low-dimensional Leibniz algebras
论文作者
论文摘要
在本文中，我们将右莱布尼兹代数的biderivations的leibniz代数进行完整分类，该代数的尺寸最多三个在字段上$ \ mathbb {f} $，并带有$ \ opperatorName {char}（char}（char}）（\ mathbb {f}）\ neq 2 $。我们描述了莱布尼兹代数的主要属性，还计算了四维DieudonnéLeibniz代数$ \ Mathfrak {D} _1 $的biderivations。最终，我们给出了一种算法，用于发现leibniz代数作为固定基础的矩阵的衍生和抗衍生物。
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 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.
