English

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}
}