Given a reductive Lie algebra g and a finite-dimensional simple g-module V, we study the category G of graded finite-dimensional modules over (g xV). This includes truncated current Lie algebras as well as those associated to folding complex simple Lie algebras. Given a face of the polytope formed by the weights of V, we introduce a partial order on the simple objects in G. Using this, for certain finite subsets of the affine weight lattice, we produce quasi-hereditary Koszul algebras of finite global dimension. (Joint with Vyjayanthi Chari and
Tim Ridenour.)
