The Homotopy Lie Algebra of a Complex Hyperplane Arrangement Is Not Necessarily Finitely Presented

Abstract

We present a theory that produces several examples in which the homotopy Lie algebra of a complex hyperplane arrangement is not finitely presented. We also present examples of hyperplane arrangements in which the enveloping algebra of this Lie algebra has an irrational Hilbert series. This answers two questions of Denham and Suciu.