The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented. (English) Zbl 1191.16009

Roos, Jan-Erik

Exp. Math. 17, No. 2, 129-143 (2008).

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

Keywords:

hyperplane arrangements; homotopy Lie algebras; Yoneda Ext-algebras; irrational Hilbert series

Citations:

Zbl 1198.17012

Software:

Macaulay2