# Lie algebra homomorphism as an scheme morphism

Assume $g$ is a finite-dimensional Lie algebra. We denote the group of Lie algebra automorphisms of $g$ by $\rm Aut_k g$. Any Lie algebra automorphism of $g$, can also be viewed as an automorphism of $g$ considered as a scheme. Why?
Simply because every linear automorphism o a vector space $V$ is an automorphism of $V$ viewed as a scheme. That $g$ is a Lie algebra or that the map is an automorphism of Lie algebras has nothing to do with this. – Mariano Suárez-Alvarez Jan 29 '13 at 22:41
Why, For every finite dimensional vector space $V$, we can viewed $V$ as an scheme? – Masoud Jan 29 '13 at 22:45
@Masoud, let $V$ be an $n$-dimensional vector space over $k,$ then $V \cong k^n$ and $k^n=\mathbb{A}_k^n=\text{Spec}(k[x_1,\cdots,x_n])$ right? – Ehsan M. Kermani Jan 30 '13 at 7:13