What is the image of an automorphism of Lie algebra?

Question

Let $L$ be a simple Lie algebra over ${\rm GF}(2)$. If $α$ is an automorphism of $L$ then for any element of $L$ we must have $α[a,b]=[α(a),α(b)]$. Now I want to have a clear understanding of image of $α$. Since $L$ is a simple Lie algebra, how can I write the image of $α$? I think it is not true to write the image of $α$ as a linear combination of basis. In fact, my confusion backs to the notion of structure constant of a Lie algebra. I know that we must consider Lie bracket and structure constants, but I need examples.