Post-Lie algebra structures on the Witt algebra

TL;DR

This paper classifies certain algebraic structures called post-Lie algebras on the Witt algebra, introduces new Lie algebras, and explores Rota-Baxter operators, advancing understanding of algebraic operations related to the Witt algebra.

Contribution

It characterizes graded and shifting post-Lie algebra structures on the Witt algebra, introduces new Lie algebras, and studies Rota-Baxter operators of weight 1.

Findings

New classes of Lie algebras constructed

Characterization of graded and shifting post-Lie structures

Analysis of Rota-Baxter operators 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.