The Centroid of Lie Superalgebras

Throughout the present paper,we mainly discuss properties of the centroid and the Killing from on the Lie Superalgebgra.KAC has giuen the concept of the centroid of the superalegbras.We give the definition of the centroid and zero-degree centroid of the Lie Superalgebras.We prove that the centroid of a simple Lie su-peralgebra is a superfield.Also we get a relation between the zero-degree centroid and the killing from of a simple Lie superalgebra.