Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators

Abstract

In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we consider weighted Rota-Baxter paired operators that induces a weighted Rota-Baxter Lie algebra and a representation of it. We define suitable cohomology for such paired operators that govern deformation.

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Cited by in corpus (3)

• Cohomologies of modified $\lambda$-differential Lie triple systems and applications
• A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
• Cohomology of morphism Lie algebras and some applications