@article{Heckenberger_Welker_2016, title={A Deformation of the Orlik-Solomon Algebra}, volume={118}, url={https://www.mscand.dk/article/view/23686}, DOI={10.7146/math.scand.a-23686}, abstractNote={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. }, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Heckenberger, István and Welker, Volkmar}, year={2016}, month={Jun.}, pages={183–202} }