A DEFORMATION OF THE ORLIK-SOLOMON ALGEBRA

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 Grobner 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 Grobner basis and hence the algebra is Koszul.