{
  "id": "math/0010168",
  "version": "v1",
  "published": "2000-10-17T22:10:24.000Z",
  "updated": "2000-10-17T22:10:24.000Z",
  "title": "Annihilators of Ideals of Exterior Algebras",
  "authors": [
    "Graham Denham",
    "Sergey Yuzvinsky"
  ],
  "comment": "18 pages; submitted to Advances in Applied Math",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "The Orlik-Solomon algebra A of a matroid is isomorphic to the quotient of an exterior algebra E by a defining ideal I. We find an explicit presentation of the annihilator ideal of I or, equivalently, the E-module dual to A. As an application of that we provide a necessary, combinatorial condition for the algebra A to be quadratic. We show that this is stronger than matroid being line-closed thereby resolving (negatively) a conjecture by Falk. We also show that our condition is not sufficient for the quadraticity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-17T22:10:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "05B35",
      "16E05"
    ],
    "keywords": [
      "exterior algebra",
      "combinatorial condition",
      "orlik-solomon algebra",
      "e-module dual",
      "annihilator ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10168D"
    }
  }
}