Abstract
The purpose of the present paper is to investigate cohomologies of relative Rota-Baxter Lie algebras with derivations and applications. First, we introduce a notion of relative Rota-Baxter LieDer pairs. Moreover, we construct cohomologies of relative Rota-Baxter LieDer pairs. Finally, we discuss abelian extensions, crossed modules and skeletal relative Rota-Baxter Lie 2-Der pairs in terms of cohomology groups.
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