A deformation of the Orlik-Solomon algebra
Combinatorics
2011-09-12 v1 Geometric Topology
Representation Theory
Abstract
A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as R-algebras. For supersolvable matroids, equivalently fiber type arrangements, there is a quadratic Groebner basis and hence the algebra is Koszul
Keywords
Cite
@article{arxiv.1109.1945,
title = {A deformation of the Orlik-Solomon algebra},
author = {Istvan Heckenberger and Volkmar Welker},
journal= {arXiv preprint arXiv:1109.1945},
year = {2011}
}