Super-biderivations And Lie Super-bialgebra Structures Of The Lie Superalgebra SBMS₃ Algebra

In this paper,we mainly study the structures and representations of the Lie superalge-bra SBMS3,which are related to those of super-Virasoro algebra.The super-biderivations and linear super-commuting maps on the super-Virasoro algebra has been studied,and all Lie super-bialgebra structures on it have been given.Based on these,we discuss the super-biderivations,linear super-commuting maps and Lie super-bialgebra structures on the Lie su-peralgebra SBMS3.There are three chapters,as follows:The first chapter is introduction,which is divided into three sections.In first section,the background of the theme researching was interpreted.In second section,we give the essential basic knowledge to complete this paper and last section,we make some symbolic instructions.There are four sections in the second chapter,we mainly introduce the super-biderivations and linear super-commuting maps on the Lie superalgebra SBMS3.In the first two sections,we give some basic concepts and general conclusions.In section 3,we determine the super-skewsymmetric super-biderivations of the Lie superalgebra SBMS3 and we find that there are no inner super-biderivations for it.Finally,in section 4,based on the result of super-biderivations,we show that all the linear super-commuting maps on it are non-standard.In third chapter,the Lie super-bialgebra structures on the Lie superalgebra SBMS3 are considered.In section 1,we introduce some basic concepts and results.In section 2,we determine the first cohomology group of the Lie superalgebra SBMS3,which is helpful in proving the later results.The method to solve it mainly based on the computation of derivations from the Lie superalgebra SBMS3 to the tensor product of its adjoint module.In section 3,we give the all Lie super-bialgebra structures on the Lie superalgebra SBMS3 and show that all such Lie super-bialgebra structures are coboundary triangular Lie super-bialgebras.