The Complexification Of N-Lie Algebras And The Classification Of Real Simple N-Lie Algebras

Throughout the present paper, the author mainly discuss the complexification of n-Lie algebras and the classification of real simple n-Lie algebras.As in Lie algebras, we give definitions of the complexification V of a real n-Lie algebra V and real forms of a complex n-Lie algebra and also make a definition of compatible complex structure. Then, by using the Killing form and non-degeneracy for the Killing form of n-Lie algebra, we investigate the semisiplicity of V, V, VR. We prove that V. V, VR ar 2-semisipLe or not 2-semisimpLe at the same time.In another part of this paper, the author's work is devoted to the classification of real simple n-Lie algebra, and to contrast the results about (n-f-l)-dimensional real simple n-Lie algebra over an algebraically closed field F with characteristic 0 in Filippove[3] with in Ling Wuxue[5], which are same in fact.