Lie Bialgebra Structures On The Schr(?)dinger-virasoro Lie Algebra

During the investigation of quantum groups, Drinfeldintroduced the notion of Lie bialgebras in1983. The relationbetween Lie bialgebra and the solution of the Yang-Baxterequation is very close. Quantization of Lie algebras andbialgebras is an important way to produce new quantum groups.So, it is meaningful to study the Lie bialgebra structures.In this paper, we study the Lie bialgebra structures on theSchr dinger-Virasoro algebra, we get its bialgebra structurethrough some special observation, comparison, and delicatetechniques, and calculate the derivation algebra. At the sametime, we know that its derivations are not all inner derivations,further more, we prove that its bialgebra structures are nottriangular coboundary.The paper consists of three sections. Its main contents andresults are summarized as follows.The first section gives introduction.Firstly, we introducetwo aspects of research and research background which is aboutthe domestic and foreign related to Lie algebras and theSchr dinger-Virasoro algebra; secondly, we were going to showthe significance and characteristic of this study. Section2recalled some definitions and results which are used in the paper. Section3studied the Lie bialgebra structures on theSchr dinger-Virasoro algebra.