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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

Citations:

Zbl 1198.17012

Software:

Macaulay2
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