The Derivations Of Lie Superalgebras And The Properties Of Complete Lie Superalgebras

Lie superalgebras arises from physics,and there is a strong association between the two.Lie superalgebras and other branches of objects like geometry and chemistry has a close relationship.Lie superalgebra has many crucial applications in other disciplines.So its research has important value and significance.In recent decades,the research of lie super algebras has developed greatly.In this paper,we discuss the derivation of some Lie superalgebras,simple Lie superalgebras and solvable Lie superalgebras.In this paper,the main content is divided into three parts.In the first part,we firstly introduce some preliminary knowledge.And we introduce the definition of Lie superalgebra,derivation superalgebra and inner derivation Lie superalgebra and give some examples.Then the derivation tower method of lie algebra is applied to the Lie superalgebra.The given Lie superalgebra with trivial centre,the Lie superalgebra which is induced by the given Lie superalgebra and its holomorph are discussed.The dimension formula of derivation of original Lie superalgebra is proved.And then the completeness of derivation of Lie superalgebra is obtained.In the second part,we introduce the definition of simple Lie superalgebra and simple complete Lie superalgebra.The simple Lie superalgebra is discussed in research method of the simple algebra.And some deduction is obtained.In the third part,we introduce the definition of Cartan Lie superalgebra and the properties of solvable complete Lie superalgebra.Through the exploration of these two kinds of Lie superalgebras,some new properties are obtained.