Classification Of Special Nilpotent Lie Superalgebras

The classification of Lie algebres is an important topic of Lie algebras' research,the same is true for Lie super algebras.In this paper,we study the classification of nilpotent Lie super al-gebras with small breadth over complex field.On the classification of Lie superalgebras,the classification of the simple Lie super algebras over algebraically closed fields of characteristic zero have been already been solved.But,at present the classification of finite dimensional nilpotent Lie superalgebras is still unresolved.Scholars usually focus on researching the classifications of nilpotent Lie superalgebras with small dimension or certain conditions.The classification of nilpotent Lie superalgebras whose dimension is less than or equal to 5 has been given over real field and complex field.Lie superalgebra is a generalization of Lie algebra.Therefore,the study of nilpotent Lie superalgebras is usually based on the method of nilpotent Lie algebras.This paper expand the concept of breadth for Lie algebras to Lie superalgebras,we study the characterization of finite dimensional Lie super algebras of breadth 1 or 2.Further,combine the characterization with basic properties of nilpotent Lie super algebras,we give a classification of finite nilpotent Lie superalgebras of breadth 1 and its classification number can be calculated directly.For breadth 2,the construction of nilpotent Lie superalgebras is more complex,so this paper only gives partial classification.