{
  "id": "1109.1945",
  "version": "v1",
  "published": "2011-09-09T08:53:05.000Z",
  "updated": "2011-09-09T08:53:05.000Z",
  "title": "A deformation of the Orlik-Solomon algebra",
  "authors": [
    "Istvan Heckenberger",
    "Volkmar Welker"
  ],
  "categories": [
    "math.CO",
    "math.GT",
    "math.RT"
  ],
  "abstract": "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 Groebner 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 Groebner basis and hence the algebra is Koszul",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-09T08:53:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "16S37",
      "16S80"
    ],
    "keywords": [
      "orlik-solomon algebra",
      "deformation",
      "quadratic groebner basis",
      "equivalently fiber type arrangements",
      "hilbert series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1945H"
    }
  }
}