KOSZUL ALGEBRAS AND HYPERPLANE ARRANGEMENTS

This is a survey to apply theory from noncommutative graded algebras to questions about the holonomy algebra and the Orlik-Solomon algebra of a hyperplane arrangement. We first recall the main properties of Koszul algebras and hyperplane arrangements. Then, we focus our interest on the class of hypersolvable arrangements which includes both the fiber-type and the generic arrangements. For these hypersolvable arrangements, the holonomy algebra is Koszul and koszulness of the Orlik-Solomon algebra characterizes the subclass of fiber-type's.