Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras

TL;DR

This paper develops a cohomology theory and deformation framework for twisted Rota-Baxter operators on 3-Leibniz and NS-3-Leibniz algebras, introducing new algebraic structures and their properties.

Contribution

It constructs an $L_$-algebra framework for twisted Rota-Baxter operators and introduces NS-3-Leibniz algebras as their underlying structure.

Findings

Established cohomology for twisted Rota-Baxter operators

Developed deformation theory from a cohomological perspective

Introduced NS-3-Leibniz algebras as a new algebraic structure

Abstract

The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted Rota-Baxter operators, and we define the cohomology of a twisted Rota-Baxter operator. Then we consider formal and order $n$ deformations of twisted Rota-Baxter operators from cohomological points of view. Finally, we introduce and study NS-3-Leibniz algebras as the underlying structure of twisted Rota-Baxter operators on 3-Leibniz algebras.