The Nilpotent Generators Of Several Classes Simple Lie Superalgebras

Since 1977,Kac gave the classification of simple Lie superalgebras over an algebraically closed field of charactic zero,the research on structure and presentation of simple Lie superalgebras has become more and more active.The automorphisms and derivations of an algebra can be determined by its generators,so the problems of generators are some very important subjects in algebra field.In this paper,we study the niilpotent generators of some simple Lie superalgebras over an algebraically closed field of charactic zero.The main content of this paper is divided into three parts.The first part we study the nilpotent generators of simple Lie superalgebra sl（m,n）.We prove that sl（m,n）can be generated by two nonzero nilpotent elements.In the special case,which is to construct a special super consistent matrix,we prove that sl（3,n）（n >1）and sl（m,2）（m > 1）can ben generated by 1.5 nonzero nilpotent generators.The second part we study the nilpotent generators of several lower-dimensional orthogonal symplectic Lie Superalgebras.We respectively to prove that osp（2,2）,osp（2,4）,osp（3,2）can be generated by two nonzero nilpotent generators.The realization method of generator is also given.The third part we prove that singular Lie Superalgebras P（2）can be generated by two nonzero nilpotent generators.The realization method of generator is also given.