Derivation Algebras Of Low Dimensional Nilpotent Lie Algebras

It is an important aspect for studying on the structure theory to research thederivation algebras of Lie algebras. The derivation algebras of semisimple Liealgebras over complex field C have been studied clearly, by contrast, the derivationalgebras of nilpotent Lie algebras have not been studied clearly, because thestructure of nilpotent Lie algebras is extremely complex. It is an effective way forcharacterizing the derivation algebra of a Lie algebra to find out some equivalentconditions of the derivation. Two step nilpotent Lie algebras is a kind of importantnilpotent Lie algebras, and it has relatively simple structure. In this paper, byingenious calculation of the matrix, a sufficient and necessary condition for thederivation of two step nilpotent Lie algebras with three dimensional center isobtained. Using the equivalent condition, the derivations of two step nilpotent Liealgebra of eight dimension with two dimension center of nonisomorphic classes arecalculated.