A Study On Several Problems Of Li Chao 's Algebraic Representation Theory

Many remarkable studies about the representations of Lie Superalgebras and Lie Superalgebra have been carried out, so it will be a new meaning to discuss the representation of classical Simple Lie Superalgebras. In this paper, we develop and study a type of indications of the classical Simple Lie Superalgebras p(n) and a representation of the classical affine Lie superalgebra (?).The organization of this paper is as follows, we first preform some preliminaries about the definitions of Lie algebras, Lie Superalgebras, representations, and the relevant concepts of the Lie Superalgebras.Next, a type of indications of the classical Simple Lie Superalgebras p(n) also is presented. Constructing classical Simple Lie Superalgebras p(n) representation,the proof ensuring the irreducible of p(n) representation is obtained.Finally, a representation of the classical affine Lie superalgebra p(n) is expanded to the classical affine Lie superalgebra (?), constituting the Classical Simple Lie Superalgebras (?), and testifying the irreducibility of the representation.