Two Families Of Infinite-dimensional Modular Lie Superalgebras

In this thesis, we mainly study two classes of infinite-dimensional Lie superalgebras Γ and (?) over a field of positive characteristic. The natural filtrations of modular Lie superalgebras of Γ-type are proved to be invariant under the automorphisms of Γ by determining ad-nilpotent elements and subalgebras generated by certain ad-nilpotent ele-ments. By the invariance of filtrations, we classify the modular Lie superalgebras of Γ-type in the sense of isomorphism. Furthermore, we obtain that the integers in the definition of infinite-dimension modular Lie superalgebras Γ are intrinsic. The infinite-dimension modular Lie superalgebras (?) are proved to be simple and the generating sets of (?) are determined. Moreover, the superderivation algebras of modular Lie superalgebras (?) are determined by using the generator sets.