TY - JOUR
AU - Heckenberger, István
AU - Welker, Volkmar
PY - 2016/06/09
Y2 - 2022/01/17
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 -