Gale duality and Koszul duality

Abstract

Given an affine hyperplane arrangement with some additional structure, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O.Comment: 55 pages; v2 contains significant revisions to proofs and to some of the results. Section 7 has been deleted; that material will be incorporated into a later paper by the same author