Two Families Of Infinite-dimensional Modular Lie Superalgebras Q And V

In this thesis, we define two classes of infinite-dimensional Lie superalgebras Q-typeand V type over a field of positive characteristic. The natural filtration of modular Liesuperalgebras of Q-type are proved to be invariant under automorphisms by studyingad-nilpotent elements. Then all the modular Lie superalgebras of Q-type are classifiedin the sense of isomorphism, that is, two Lie superalgebras of Q-type are isomorphic ifand only if the integers in the definition of these Lie superalgebras are intrinsic. On thebase of modular Lie superalgebras of Q-type, we define a family of modular Lie super-algebras of V-type. The simplicity is proved. By characterizing ad-nilpotent elementsand determining certain invariants such as subalgebras generated by some ad-nilpotentelements, the invariance of the natural filtration of modular Lie superalgebras of V typeis investigated and thereby an important property of these Lie superalgebras is obtained.