Cohomology Of Even Center Five Dimensionnal Nilpotent Lie Superalgebras

In the study of Lie algebras and Lie superalgebras,cohomology is an important research topic.Nilpotent Lie superalgebras are a special kind of Lie superalgebras.In this paper,by constructing the isomorphic complex of Chevalley-Eilenberg cochain complex of Lie superalgebras,we calculate the cohomology of five dimensional nilpotent Lie superalgebras over complex field C,which are nontrivial and indecomposable but have only even center.