Lie Superalgebras Of Cartan Type

This thesis is about the structure theory of various Cartan-type Lie superalgebras.In particular, the generators, derivations, fltrations and automorphisms of these algebrasare studied. The thesis consists of two parts. The frst part deals with two families offnite-dimensional Cartan-type Lie superalgebras H((?)) and HO((?)) over a feld of primecharacteristic. The generators and homogeneous superderivations of modular Lie super-algebras H((?)) and HO((?)) are obtained. The structures of derivation superalgebras ofH((?)) and HO((?)) are determined completely. Moreover, H((?)) and HO((?)) are shown tobe extensions of Lie superalgebrasH (n) and HO(n, n,(?)), which were constructed previ-ously by Kac and Liu-Zhang, respectively.The part two is devoted to the study of the Lie superalgebras H(Λ) and HO(Λ) offormal vector felds. The ad-quasi-nilpotent elements and subalgebras generated by cer-tain ad-nilpotent elements are investigated. It is established using the ad-quasi-nilpotentelements that the natural fltrations of H(Λ) and HO(Λ) of formal vector felds are invari-ant under automorphisms. Furthermore, the automorphism groups of H(Λ) and HO(Λ)are proved to be isomorphic to the corresponding admissible automorphism groups of thebase superalgebra Λ(n, m).