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