The Module Structure Of W_[0] Of Modular Lie Superalgebra W（1,2,（?）） Of Cartan Type

Modular Lie superalgebras mainly deal with three questions:classification, repre-sentation and structure. The representation of modular Lie superalgebras are the imp-ortant part of modular Lie superalgebars. This paper gives some results in order to so-lve the representation of modular Lie superalgebras.LetF be an algebraically closed field with char F=p>2and Z2be the residue c-lass ring module2with the elements0and1. LetU(m) denote a divided power algebra over F with generated elements{x(a)｜α∈N0m and A(n) denote the Grassmann algebra in n variables over F. We denote A(m,n)=U(m)(?)(n),then A(m,n) is a supe-ralgebra with the Z2-gradation. The present thesis is devoted to studying modular Lie superalgebras W(1,2,1) and W(2,1,1) of Cartan type, from the divided power algebra U(m), exterior algebra A(n) and derivations.The concrete contents of this thesis are listed as follows:Chapter one is devoted to introduce the background of research,general develop-ment and the latest results of the theory of modular Lie superalgebras.In Chapter two, we introduce some essential definitions and preliminary theore-ms related to this thesis, suppose thatW(m,n,t) is a modular Lie superalgebra of Car-tan Type and give some results.In Chapter three, the module structure of W[0] of W(1,2,1) is discussed.In Chapter four, the module structure of W[0] of W(2,1,1) is discussed.In Chapter five, we give some conclusions and open problems.