3.This paper, by the method of generator and the defining relation embed a class of finite dimension Cartan solvable Liealgebra into a semisimple Liealgebra and prove:1) Any finite cartan solvable Liealgebra is the Borel subalgebra of some semisimple Liealgebra;
6.In this paper, the holomorph h(g 0) of a Liealgebra g 0 which is a driect sum of a Heisenberg algebra and an abelian Liealgebra is given. The derivation algebra Derh(g 0) of h(g 0) is also given. We prove that h(g 0) is not a complete Liealgebra, but Derh(g 0) is a simple complete Liealgebra.
7.In this paper,the devivation algebra Dery of Liealgebra is given,y which is thd direct sum of a Heisenbery algebra H and an abelian &. It is proved that Dery id a simple complete Liealgebra.
