Derivation Algebras Of 6-dimensional 4-Lie Algebras

N-Lie algebra is the generalization fo a Lie algebra to the case where the fundamental multiplication operation is n-ary. But the structure of them is diffierent. In rencent years, much interest has been shown in the study of n-Lie algebras, which is due to its wide applications in geometry and physics. As we well know, by means of the derivation, that n-Lie algebras can be applied to the Lie groups, and through the quasi-derivation, a new metric n-Lie algebra can be constructed by a metric Lie algebra or a metric (n-1)-Lie algebra, etc. Therefore, the derivation of n-Lie algebras is an important tool in studing the structural theory.In the paper the structure of derivation algebras and inner derivation algebras of 6-dimensional 4-Lie algebras over an algebraically closed field of characteristic zero are investigated. The concrete expression of ever derivation and inner derivation are given.There are three sections in the paper. Some basic notions are introduced in the first part introduces. In section 2, the inner derivation algebras of ever class of 6 dimensional 4-Lie algebras are discussed. The derivation algebras are studied in section 3.