University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Representation Theory

Abstract: Given a simple Lie algebra g and a finite-dimensional simple g-module V, we study the category G of graded finite-dimensional modules of the corresponding semidirect product Lie algebra. This framework includes the truncated current Lie algebras as well as those associated to folding of 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. For certain finite subsets of the affine weight lattice, we produce Koszul algebras of finite global dimension equal to the number of weights of V which are on the face. This is joint work with Vyjayanthi Chari and Tim Ridenour.