{
  "id": "0803.0064",
  "version": "v2",
  "published": "2008-03-01T13:14:02.000Z",
  "updated": "2008-06-10T10:25:58.000Z",
  "title": "Homological properties of Orlik-Solomon algebras",
  "authors": [
    "Gesa Kaempf",
    "Tim Roemer"
  ],
  "comment": "27 pages, minor modifications",
  "journal": "Manuscr. Math. 129, No. 2, 181-210 (2009)",
  "categories": [
    "math.CO",
    "math.AC",
    "math.RA"
  ],
  "abstract": "The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our results to Orlik-Solomon algebras of matroids and give formulas for the complexity, depth and regularity of such rings in terms of invariants of the matroid. Moreover, we characterize those matroids whose Orlik-Solomon ideal has a linear projective resolution and compute in these cases the Betti numbers of the ideal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-10T10:25:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "16E05",
      "52C35",
      "13P10",
      "16W50"
    ],
    "keywords": [
      "orlik-solomon algebra",
      "study homological properties",
      "complexity",
      "betti numbers",
      "regularity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0064K"
    }
  }
}