Deformations of relative Rota-Baxter operators on Leibniz Triple Systems

2022/08/15 by Wu, Xueru, Ma, Yao, Chen, Liangyun
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2210.04589

Abstract

In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz triple systems. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, formal deformations and extendibility of order n deformations of a relative Rota-Baxter operators are also characterized in terms of the cohomology theory. We also consider the relationship between cohomology of relative Rota-Baxter operators on Leibniz algebras and associated Leibniz triple systems.

Related

• Relative Rota-Baxter systems on Leibniz algebras
• Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras
• Cohomology of modified Rota-Baxter Leibniz algebra of weight λ
• Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras
• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras