Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

In this paper, first we give the notion of a representation relative Rota-Baxter Lie algebra and introduce cohomologies with coefficients in representation. Then classify abelian extensions algebras using second cohomology group, skeletal 2-algebras third group as applications. At last, established general framework representations algebras, which is consistent associative literature, Applications are also given to classifying 2-algebras.