Some properties of the family $\Gamma $ of modular Lie superalgebras

summary:In this paper, we continue to investigate some properties of the family $\Gamma $ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras $\Gamma $ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable