Filtrations Of Modular Lie Superalgebras Of O-type

This paper considers a family of finite-dimensional Lie superalgebras of O-type over an algebraically closed field of characteristic p > 3. For each algebra in the family, the filtration of O is determined and we prove that it is invariant under the automorphism group of O. Then an intrinsic property is proved by the invariance of the filtration;that is, the integers in the definition of O are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism.