Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.
In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.
In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring.