On the modular Lie superalgebra Ω

A class of finite-dimensional simple modular Lie superalgebra Ω was constructed and its derivation superalgebra was determined in Zhang and Zhang (2009) [24]. The purpose of the present paper is to continue the investigation of finite-dimensional modular Lie superalgebra Ω. A nonnatural filtration of finite-dimensional modular Lie superalgebra Ω over a field of positive characteristic is determined. It is proved that the nonnatural filtration of Ω is invariant under the automorphism group of Ω. Moreover, we obtain the sufficient and necessary conditions of , i.e., we classified the Lie superalgebra of Ω type.