| Lie superalgebra deals mainly with three questions: classification, representation and structure. V.G.Kac gave the classification of finite-dimensional simple Lie superalgebras over a field of characteristic zero in 1977. But the study of modular Lie superalgebras just began in recent ten years. The results are few. Up to now, the classification of modular Lie superalgbras is an open problem. This paper gives some results in order to solve the classification and structure of Lie superalgbras.The definition of a Lie superalgebra of Cartan type was given by Prof. Zhang Yongzheng in 1997. The finite-dimensional Lie superalgebras of Cartan type are divided into four classes: W, S, Hand K. The four classes of Lie superalgebras are simple. The generated sets and derivation algebra of H in the situations of charF = p>3,m>2,n>l are determined by Wang Ying in 2004. This paper mainly gives the derivation algebra of H in the special cases of charF = p = 3,m = 2,n = l. Thus the derivation algebras of H are determined completely.Generalized Simple Weyl type algebras were given by Prof. Su Yucai and Zhao Kaiming in 2000. They are in general nongraded and nonlinear. The weyl algebras are important because some classical Lie algebras are equivalent to that of the Weyl type algebras. However, the structure theory of generalized Weyl type algebras does not seem to be well-developed. Lie superalgebras are important in physics and Lie superalgebras depend on Lie algebra deeply, so we consider Weyl type Lie superalgbras naturally. This paper gives the difinition of Weyl type Lie superalgbra in the same ways and gives a necessary and sufficient condition here for this Lie superalgebra to be simple. |
