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# Cohomology of modified Rota-Baxter Leibniz algebra of weight $\kappa$

Bibhash Mondal and Ripan Saha

Submitted on 15 November 2022

## Abstract

Rota-Baxter operators have 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 which controls the deformation. Finally, as an application, we characterize equivalence classes of abelian extensions in terms of second cohomology groups.

## Preprint

Comment: 18 pages

Subject: Mathematics - Rings and Algebras