The Left-symmetric Algebra And Conformal Algebra Of Schr?dinger-virasoro Lie Algebra

We classify all the compatible left-symmetric algebra structures on (?) with natural grading conditions,focus on compatible left-symmetric algebra structures on Schr?dinger-Virasoro Lie algebra (?),and provides a natural and intrinsic characterization of the relationship between the left-algebras and Schr?dinger-Virasoro Lie algebras.Furthermore,the research of Lie conformal algebra has promoted the research of infinite dimensional Lie algebras,which provides a new and important tool for delving into infinite dimensional Lie algebras.By the results of formal distribution Lie algebras,we construct the rank three conformal algebra of a kind of Schr?dinger Virasoro algebra.