| Affiliation: | a Department of Mathematics and Statistics, University of Massachusetts, United States
b Department of Mathematics, Stanford University, United States
c Department of Mathematics, University of Oregon, United States
d Department of Mathematics, Massachusetts Institute of Technology, United States |
| Abstract: | Given a hyperplane arrangement in an affine space equipped with a linear functional, 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. |
