Derivation Algebras Of A Class Of 5 Dimensional 3-lie Algebras

The n-Lie algebra is a generaliztion of Lie algebra, which is an algebraic sys-tem with an n-ary linear operation. The n-Lie Algebra has its back ground in mechanics and manifolds. So it is necessary to study the structure and applications of them. The paper mainly concerns structure of a class of 5 dimensional 3-Lie al-gebras and their derivation algebras. The structure of 5-dimensional 3-Lie algebras over Z2 with 1 and 2-dimensional derived algebras are studied respectively. We also give the concrete expression of each derivations.The paper consists of four sections. The back ground and development of n-Lie algebras are introduced in the Section 1. In the Section 2 we give some definitions and results of n-Lie algebras which are used in the paper. In the Section 3 we study the derivation algebras of 5 dimensional 3-Lie algebras over Z2 with 1 and 2-dimensional derived algebras. We summarize the results of the paper in the Section 4.