Abstract: The authors studied some properties on n + 1 dimensional n - Lie algebras, and we proved that when dimension of dim A 1＞ 1, the dimension of Cartan subalgebra of A is n - 1. And also proved that n + k dimensional n - Lie algebra is simple if and only if it has not ideals that the dimension are not more than k and A = [ A A ], and other results about Cartan subalgebras of n - Lie algebras.

Key words: n - Lie algebra, Cartan subalgebra, semi - simple, n - Lie algebras.Deceived:2002 - 01 - 15