The Studies Of Two Families Of Modular Lie Superalgebras

In this thesis, we study two families of modular Lie Superalgebras. First we primarilydiscuss the structure of modular Lie superalgebras ? in the infinite-dimensional case.The simplicity of infinite-dimensional modular Lie superalgebras ? are demonstrated.Besides, their generating sets are investigated. Furthermore, the superderivation algebrasof infinite-dimensional modular Lie superalgebras ? are determined. Then we primarilystudy the graded modules of the finite-dimensional odd Hamiltonian superalgebras. Byusing the method of mixed product, we prove that if V is an L-module, then the mixedproduct?V is the Z-graded HO(n, n, t)-module and HO(n, n, t)-module.