In this paper, we introduce the cohomology theory of relative Rota–Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota–Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations. Formal deformations and extendibility of order [Formula: see text] deformations of a relative Rota–Baxter operator are also characterized in terms of the cohomology theory.

中文翻译：

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莱布尼茨代数上相对Rota-Baxter算子的变形

在本文中，我们介绍了莱布尼茨代数上相对Rota-Baxter算子的上同调理论。我们使用上同调方法来研究相关 Rota-Baxter 算子的线性和形式变形。特别是，引入了 Nijenhuis 元素的概念来表征微不足道的线性变形。阶的形式变形和可扩展性 [公式：见正文] 相对 Rota-Baxter 算子的变形也可以根据上同调理论进行表征。