The Poisson Structures On A Class Of Infinite Dimensional Lie Algebras

In this paper,we study the Poisson algebra structures on a class of infinite dimensional Lie algebras,which are called the twisted deformative Schrodinger-Virasoro algebras.Poisson algebras are the algebras having a Lie structure and an associative algebra structure together with the Leibniz law.The twisted deformative Schrodinger-Virasoro algebras are an important class of infinite Lie algebras,which are obtained by deforming of the twisted Schrodinger-Virasoro algebras,and they contain Schrodinger algebras and Virasoro algebra as subalgebras.In this paper,we determine the Poisson algebra structures on these Lie algebras.