TY - JOUR AU - Heckenberger, István AU - Welker, Volkmar PY - 2016/06/09 Y2 - 2024/03/29 TI - A Deformation of the Orlik-Solomon Algebra JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 118 IS - 2 SE - Articles DO - 10.7146/math.scand.a-23686 UR - https://www.mscand.dk/article/view/23686 SP - 183-202 AB - A deformation of the Orlik-Solomon algebra of a matroid $\mathfrak{M}$ 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 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. ER -