Research On Some Properties Of The Finite-dimensional Simple Modular Lie Superalgebra (?)(n,m)

In this thesis, we study some properties of the finite-dimensional simple modular Lie superalgebras w(n,m), the main contents are as follows.In Chapter 1, we first introduce the research status of the modular Lie superalgebras in China and abroad. Then we list the research results about the associative form and restrictiveness of the finite-dimensional simple modular Lie superalgebras in China and abroad. At the end of the chapter 1, we introduce the main contents of this thesis. In Chapter 2, , we first briefly state some related concepts and conclusions about modular Lie superalgebras, which will be used in this thesis, then we review the modular Lie superalgebra (?)(n,m) . In Chapter 3, we first prove that (?)(n,m)is a Z-graded Lie superalgebra,then we confirm a maximal subalgebra W[0]of (?)(n,m). In Chapter 4, we prove that (?)(n,m) has a nonsingular associative form,and it is a restrictive Lie superalgebra. At the end of this thesis, other research problems of (?)(n,m) such as cohomology group etc. are outlooked.