Super-biderivations And Lie Super-bialgebra Structures On The Two Dimensional Supersymmetric Galilean Conformal Algebra

In this thesis,we mainly study the structure of the two dimensional supersymmetric Galilean conformal algebra.The two dimensional supersymmetric Galilean conformal algebra is obtained by contraction of the two copies of the super-Virasoro algebra.In recent years,the structures and representations of the super-Virasoro algebra have been studied by many scholars.Based on these,we study super-biderivations and Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra.There are three chapters,as follows:The first chapter is the introduction,which is divided into three sections.In Section 1,we mainly introduce the background of the research topic.Some basic knowledge is given in Section 2.In order to simplify the writing,we give the symbol descriptions in Section 3.There are three sections in the second chapter,we mainly study the super-biderivations on the two dimensional supersymmetric Galilean conformal algebra.In the first two sections,we mainly introduce some basic concepts and general conclusions.In Section 3,we determine each super-skewsymmetric super-biderivation of the two dimensional supersymmetric Galilean conformal algebra.In particular,we find that there exist non-inner super-biderivations on the two dimensional supersymmetric Galilean conformal algebra.In the third chapter,we mainly determine the Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra.In Section 1,we give the basic concepts and results which are used in our discussions.In Section 2,by computing derivations from the two dimensional supersymmetric Galilean conformal algebra to the tensor product of its adjoint module,we determine the first cohomology group of the two dimensional supersymmetric Galilean conformal algebra.In Section 3,we give the all Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra and obtain that such Lie super-bialgebra structures are triangular coboundary Lie super-bialgebra.