Cartan Subalgebras of a Semi-restricted Lie Algebra

In this paper we show that if a semi-restricted Lie algebra L has an one dimensional toral Cartan subalgebra, then L is simple and $L\simeq_-sl(2)$ or $W(1:\underline{1})$. And we study that if L is simple but not simple and H is 2-dimensional, then H is a torus.