The Graded Modules Of Simple Modular Lie Superalgebras HO,SHO,KO

This paper aims to talk about the graded modules of the finite-dimensional simple modular Lie superalgebras HO and SHO by using the methods of extension and mixed product realization.Meanwhile by using the methods of professor Shen’s mixed product realization and professor Hu’s method,the graded module of the finite-dimensional simple modular Lie superalgebra KO is studied.Besides,by taking advantage of the structures of HO0,SHO0 and KO0,we obtain the isomorphic matrix algebras and their root systems.Finally,we discuss how they influence the reducibilities of the graded modules of HO,SHO and KO.