Weighted relative Rota-Baxter operators on Leibniz algebras and Post-Leibniz algebra structures

TL;DR

This paper explores weighted relative Rota-Baxter operators on Leibniz algebras, introduces their cohomology and deformations, and establishes post-Leibniz algebras as the underlying structure, expanding algebraic theory.

Contribution

It defines cohomology for weighted relative Rota-Baxter operators on Leibniz algebras and introduces post-Leibniz algebras as a new structural framework.

Findings

Cohomology of weighted relative Rota-Baxter operators is established.

Deformations of these operators are studied.

Post-Leibniz algebras are introduced as the structural basis.

Abstract

Leibniz algebras are non-skewsymmetric analogue of Lie algebras. In this paper, we consider weighted relative Rota-Baxter operators on Leibniz algebras. We define cohomology of such operators and as an application, we study their deformations. Finally, we introduce and study post-Leibniz algebras as the structure behind weighted relative Rota-Baxter operators.