A Class Of Simple Lie Superalgebra Of Weyl Type

Lie superalgebras deal mainly with three questions: classification, representation and structure. Simple Lie superalgebras are the important part of the construction theorems of Lie superalgebras. This paper gives some results in order to solve the structure of modular Lie superalgbras.Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.The concrete contents of this thesis are listed as follows:Chapter 1 is devoted to introduce the context of research, general development and the latest results of the thoery of simple Lie superalgebras. And the problems that will be studied in this paper are presented.In Chapter 2, we introduce some essential definitions and preliminary theorems related to this thesis and the classical results of simple Lie superalgebras, which is the way of constructing the four classes of Lie superalgebras of Cartan type and proving the simplicity of them.In Chapter 3, we introduce the construction of simple Lie algebras and simple Lie superalgebras which are not isomorphisic to each other. We observe the way of construction, the sufficient and necessary conditions and the proving methods.In Chapter 4, from the way of the construction of simple Lie algebras and simple Lie superalgebras introduced above, especially the way of the construction which was adopted by Su Yucai and Zhao Kaiming, we construct a class of simple Lie superalgebra of Weyl type and simple associative superalgebra of Weyl type, and prove the simplicity of them.