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 dimA=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?