A Deformation of the Orlik-Solomon Algebra

  • István Heckenberger
  • Volkmar Welker


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.
How to Cite
Heckenberger, I., & Welker, V. (2016). A Deformation of the Orlik-Solomon Algebra. MATHEMATICA SCANDINAVICA, 118(2), 183-202. https://doi.org/10.7146/math.scand.a-23686