| The classification of n-Lie algebras is an important subject in the structural theory of n-Lie algebras. Up to now, few works have been done about the classification of n-Lie algebras.Only the (n+1) dimensional and (n+2)-dimensional n-Lie algebras over the algebraically closed field of characteristic 0,and that over the complete field of characteristic 2 have been classified.In this paper,the classification of 6 dimensional 3-Lie algebras over an algebraically closed field of characteristic zero are studied.By means of the properties of maximal subalgebras of 3-Lie algebras and the classification of 5 dimensional 3-Lie algebras,the complete classification of 6 dimensional 3-Lie algebras which with 1 or 2 dimensional derived algebras are obtained respectively. Further more, the nilpotency and solvability of every class are discussed.The orgnization of the paper is as follows.The background and development of n-Lie algebras are introduced in the Introduction.Some definitions,notation and some basic results are recalled in the Section 1.The classification of 6 dimensional 3-Lie algebras with 1 and 2 dimensional derived algebra are classified in Section 2 and 3,respectively. |
