A Deformation of the orlik-solomon algebra

Abstract

A deformation of the Orlik-Solomon algebra of a matroid - 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 Gröbner 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 Gröbner basis and hence the algebra is Koszul.