Relative Rota–Baxter Leibniz algebras, their characterization and cohomology

Recently, relative Rota–Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider Leibniz (rRB algebras) as object our study. We construct an L∞-algebra that characterizes rRB its Maurer–Cartan elements. Then define representations algebra and introduce cohomology with coefficients a representation. As applications cohomology, study deformations abelian extensions algebras.