The Double Derivations Of A Kind Of Deformed Schrödinger-Virasoro Algebra

The structure and representation theory of Lie algebras are the hot research directions in recent years.Considering that the infinite dimensional Schr?dinger Lie algebras and Virasoro algebras play an important role in many fields of mathematics and physics.For a,b?C,s=0 or 1/2,the deformative Schr?dinger-Virasoro algebra W(a,b,s)is the semi-direct product Lie algebra of the Witt algebra and its tensor density module.It contains W-algebra W(a,b)as its subalgebras,and Schr?dinger-Virasoro algebra is his special case.In Lie group,Post-Lie algebra is a more general form of Pre-Lie algebra and LR-algebra.It is closely related to Rota-Baxter algebra,classical Yang-Baxter modified equation and integral system.In this paper,all biderivations of W(a,b,s)are determined.It is observed that these Lie algebras have rich variety of symmetric(and skewsymmetric)non-inner biderivations.As an application,the commutative post-Lie algebra structures on W(a,b,s)are obtained.