The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented. (English) Zbl 1191.16009
Summary: 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 G. Denham and A. I. Suciu [Mich. Math. J. 54, No. 2, 319-340 (2006; Zbl 1198.17012)].
MSC:
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 17B70 | Graded Lie (super)algebras |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
| 32S22 | Relations with arrangements of hyperplanes |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
| 55P62 | Rational homotopy theory |
| 16S37 | Quadratic and Koszul algebras |
| 17B55 | Homological methods in Lie (super)algebras |
