{
  "id": "1110.4966",
  "version": "v9",
  "published": "2011-10-22T11:33:18.000Z",
  "updated": "2012-10-23T11:05:20.000Z",
  "title": "Differential operators on projective modules",
  "authors": [
    "Helge Maakestad"
  ],
  "comment": "Corollaries 3.3, 3.4 and 3.5 removed because of an error",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "In this paper we give explicit formulas for differential operators on a finitely generated projective module E on an arbitrary commutative unital ring A. We use the differential operators constructed to give a simple formula for the curvature of a connection on a Lie-Rinehart algebra in terms of the fundamental matrix of E. This gives an explicit formula for the curvature of a connection on E defined in terms of an idempotent for E. We also consider the notion of a stratification on the module E induced by a projective basis. It turns out few stratifications are induced by a projective basis.",
  "revisions": [
    {
      "version": "v10",
      "updated": "2020-11-12T12:31:51.000Z",
      "journal": null,
      "doi": null,
      "authors": [
        "Helge Øystein Maakestad"
      ]
    },
    {
      "version": "v9",
      "updated": "2012-10-23T11:05:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "14F40"
    ],
    "keywords": [
      "differential operators",
      "projective module",
      "explicit formula",
      "projective basis",
      "simple formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.4966M"
    }
  }
}