Ad-nilpotent Elements, Filtration And Classification Of Infinite-dimensional Lie Superalgebra Ω

In this thesis, we mainly consider modular Lie superalgebras, i.e., Lie superalgebra over a field of positive characteristic. The natural fitration of the infinite-dimensional modular Lie superalgebras Ω is proved to be invariant under the automorphism group of Lie superalgebras Ω by investigating ad-nilpotent elements. furthermore, by the invariance of filtration, all the infinite-dimensional modular Lie superalgebras Ω are classified in the sense of isomorphism, that is, the parameters in the definition of Ω are intrinsic.