The Natural Filtration Of The Finite-Dimensional Modular Lie Superalgebras H(n,m)

Supposed F is a field with characteristic p >2. First we define the associative superalgebra U and its partial differential Di . Than we construct a class of finite dimensional modular Lie superalgebras H ( n , m ), its structure as well as its Z-gradation are given. Meanwhile its basic properties are discussed. Taking use of the conclusions of the derivation superalgebra of H ( n, m ), we prove that the natural filtration of H ( n, m )is invariant. Finally get the sufficient and necessary conditions of that H ( n,m)and H ( n',m')are isomorphic.