Kindly asking for any hints about the following questions:
Suppose, $X$ be an arbitrary scheme over an algebraically closed field $k$.
1- In general, what is the structure of $A= \mathcal{O}_X(X)$?
2- If $g$ be an finite-dimensional Lie algebra over k. Then $g$ is naturally equipped with the structure of an affine algebraic scheme. Define $ M(X,g) $ be the Lie algebra of regular functions on $X$ with values in $g$ (equivalently, the set of morphisms of schemes $X \rightarrow g$), then proof that there is an isomorphism $M(X,g) \cong g⊗A$ of Lie algebras over $A$ and hence also over $k$.
Thanks for your help!
