  Let $\mathfrak g$ be a complex simple Lie algebra and let $\Psi$ be an
extremal set of positive roots. One associates with $\Psi$ an infinite
dimensional Koszul algebra $\bold S_\Psi^{\lie g}$ which is a graded subalgebra
of the locally finite part of $((\bold V)^{op}\tensor S(\lie g))^{\lie g}$,
where $\bold V$ is the direct sum of all simple finite dimensional $\lie
g$-modules. We describe the structure of the algebra $\bold S_\Psi^{\lie g}$
explicitly in terms of an infinite quiver with relations for $\lie g$ of types
$A$ and $C$. We also describe several infinite families of quivers and finite
dimensional algebras arising from this construction.
