Deformations of relative Rota–Baxter operators on Leibniz algebras.

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 n deformations of a relative Rota–Baxter operator are also characterized in terms of the cohomology theory. [ABSTRACT FROM AUTHOR]