Post-Lie Algebra Structures on the Witt Algebra

Abstract

In this paper, we characterize the graded post-Lie algebra structures and a class of shifting post-Lie algebra structures on the Witt algebra. We obtain some new Lie algebras and give a class of their modules. As an application, the homogeneous Rota-Baxter operators and a class of non-homogeneous Rota-Baxter operators of weight 1 on the Witt algebra are studied.