  We introduce and investigate a functorial construction which associates
coherent sheaves to finite dimensional (restricted) representations of a
restricted Lie algebra $\mathfrak g$. These are sheaves on locally closed
subvarieties of the projective variety $\mathbb E(r,\mathfrak g)$ of elementary
subalgebras of $\mathfrak g$ of dimension $r$. We show that representations of
constant radical or socle rank studied in \cite{CFP3} which generalize modules
of constant Jordan type lead to algebraic vector bundles on $\mathbb
E(r,\mathfrak g)$. For $\mathfrak g = Lie(G)$, the Lie algebra of an algebraic
group $G$, rational representations of $G$ enable us to realize familiar
algebraic vector bundles on $G$-orbits of $\mathbb E(r, \mathfrak g)$.
