Let $A$ be a finite dimensional algebra over finite field (not necessarily associative). Then $A$ is said to be homogeneous if $Aut(A)$ acts transitively on the one-dimensional subspace of A. If A is homogeneous then either $A^2=0$ or $\text{dim}A=1$. Now I want to check this property for a finite dimensional simple Lie algebra over $GF(2)$. I want to know whether a simple lie algebra over $GF(2)$ is homogeneous or not?