Holonomy Lie algebra of a geometric lattice
Geometric Topology
2023-02-03 v2 Combinatorics
Rings and Algebras
Abstract
Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie algebra is an almost-direct product of the holonomy Lie algebra of the sublattice and a free Lie subalgebra. This yields the structure of the holonomy Lie algebra of a finite hypersolvable (including supersolvable) lattice. As applications, we obtain the structure of the holonomy Lie algebra of (the Salvetti complex of) a supersolvable oriented matroid, and that of a hypersolvable arrangement.
Cite
@article{arxiv.1908.05826,
title = {Holonomy Lie algebra of a geometric lattice},
author = {Weili Guo and Ye Liu},
journal= {arXiv preprint arXiv:1908.05826},
year = {2023}
}
Comments
14 pages, 3 figures. New title and generalized results