Derivation Algebras Of Three Step Low Dimensional Nilpotent Lie Algebras

Derivation algebra is an important aspect of the study on the structure of Lie algebra and it’s also important in other objects such as differential geometry,theoretical physics and so on.Therefore,it’s necessary to study the Lie derivation algebra.As we all know,the derivation of semi simple Lie algebra has been studied completely,by contrast,that of nilpotent Lie algebra hasn’t been clear until now and the main reason is that its structure is complex extremely.For characterizing the derivation of Lie algebra,it’s an effective way to find out some equivalent conditions about it.In this paper,we discuss the derivation algebra of three step 6-dimensional nilpotent Lie algebra over fields of characteristic not 2 about which we get some equivalent conditions by the method of matrix representation and,using these results,characterize the derivation specifically.