  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.
