In this note, we interpret Leibniz algebras as differential graded Lie algebras. Namely, we consider two functors from the category of Leibniz algebras to that of differential graded Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley-Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in arXiv:1904.00121 [math.KT].

中文翻译：

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微分分级李代数和莱布尼茨代数上同调

在本笔记中，我们将莱布尼茨代数解释为微分分级李代数。即，我们考虑从莱布尼茨代数范畴到微分分级李代数范畴的两个函子，并表明它们自然地产生了莱布尼茨上同调和 Chevalley-Eilenberg 上同调。作为应用，我们证明了 Pirashvili 在 arXiv:1904.00121 [math.KT] 中陈述的猜想。