关键词: 李超代数, 型心, 零次型心, 双线性型, 超域

Abstract: Throughout the present paper, we mainly discuss properties of the centroid and the Killing fromon the Lie Superalgebra. KAC has given the concept of the centroid of the superalgebras. We give the definitionof 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 simpleLie superalgebra.

Key words: Lie superalgebra, centroid, zero-degree centroid, Killing form, superfield