Post-Lie Algebra Structure On Virasoro Algebra

The Virasoro algebra and (?)(2,2)algebra are infinite dimensional Lie algebras which have been widely used in two-dimensional conformal field theory and in string theory.The post-Lie algebra appears in many areas of mathematics and physics.In this paper,we characterize the graded post-Lie algebra structures on the Virasoro algebra and (?)(2,2)algebra.On this basis,we characterize some new Lie algebraic Structures,we also compute Rota-Baxter operators on Virasoro algebra and (?)(2,2)algebra.