Post-Lie Algebra Structure For Lie Algebras Related To Virasoro Algebras

Heisenberg-Virasoro algebra HV and Schr(?)dinger-Virasoro algebra SV are two classes of important infinite-dimensional Lie algebras,both of which are extensions of Virasoro algebra and attract many algebra scholars.Post-Lie algebra is a class of important non-associative algebras,which has a wide range of applications in mathematics and mathematical physics.Finding the post-Lie algebra structures on a given Lie algebra is an important research topic.This paper is divided into two parts:in the first part,the post-Lie algebra structures on HV are characterized,as an application,we give the characterization of the homogeneous Rota-Baxter operators on HV.In the second part,the corresponding post-Lie algebra structures on SV are characterized,and the forms of homogeneous Rota-Baxter operators on SV are found.