  Rota-Baxter operators have been paid much attention in the last few decades
as they have many applications in mathematics and physics. In this paper, our
object of study is modified Rota-Baxter operators on Leibniz algebras. We
investigate modified Rota-Baxter Leibniz algebras from the cohomological point
of view. We study a one-parameter formal deformation theory of modified
Rota-Baxter Leibniz algebras and define the associated deformation cohomology
that controls the deformation. Finally, as an application, we characterize
equivalence classes of abelian extensions in terms of second cohomology groups.

Rings and Algebras