The 5-dimensional 3-Lie Algebras With Nil Center

N-Lie algebra is a generaliztion of Lie algebra, which is an algebraic system with an n-ary multilinear operation. The structure of n-Lie Algebras is great different from that of Lie algebras. So it is necessary to study the structure and applica-tions of n-Lie algebras. This paper mainly concerns the derivation algebras with 2-dimensional derived algebras over the field Z2.We also give the concrete expres-sion of each derivation. At the last of the peper, we prove that there does not exist 3-Lie algebras with simple derivation algebras over a field of characteristic 2.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 basic results of n-Lie algebras which are used in the paper. In the Section 3 we study the structure of 5-dimensional 3-Lie algebras over Z2 with 2-dimensional derived algebras and nil center.