The Irreducibility Of Some Modules Over Modular Lie Superalgebras ????n?_? And ????2?

Lie superalgebras and Lie algebras play an important role in mathematical physics.The study of Lie superalgebras becomes one of the most active fields in mathematics.Over the last several decades,the study on Lie superalgebras has attracted extensive attension of math,and phys[9-13].According to the characteristics of the base fields,Lie superalgebras are divided into characteristic zero Lie superalgebras and characteristic p Lie super algebras,Lie superalgebras over fields of characteristic p>0 are also called modular ones.Modular Lie superalgebras mainly deal with three questions:representation,structure and appl.The representation theory of modular Lie superalgebras are the important part of modular Lie superalgebras.Let F be an algebraically closed field with char F?p>2,and Z2 be the residue class ring module 2 with the elements ??? and ???,??n?denote the Grassmann algebra in n variables over F.This paper gives some results on the module structure over ????n?0 and P?2?.The contents of this thesis are listed as follows:Chapter one is devoted to introducing the background of the research,general development and on some latest results of the theory of modular Lie Superalgebras.In Chapter two,we introduce some essential definitions and preliminary theorems related to modular Lie superalgebras over ????n?.In Chapter three,the module structure of g_? over ????2?is discussed.In Chapter four,the module structure of g_? over ????3?is discussed.In Chapter five,the module structure of ????2?over 9[?2|2?is discussed.