{
  "id": "0911.0633",
  "version": "v1",
  "published": "2009-11-03T17:54:35.000Z",
  "updated": "2009-11-03T17:54:35.000Z",
  "title": "Existence of Auslander-Reiten sequences in subcategories",
  "authors": [
    "Puiman Ng"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "This paper studies the existence of Auslander-Reiten sequences in subcategories of mod A, where A is a finite dimensional algebra over a field. The two main theorems give necessary and sufficient conditions for the existence of Auslander-Reiten sequences in subcategories. Let M be a subcategory of mod A closed under extensions and direct summands, and let X be an indecomposable module in M such that Ext^{1}(X, X') is not zero for some X' in M. Then the following are equivalent: (i) DTrX has a precover in the stable category of mod A, (ii) There exists an Auslander-Reiten sequence 0 --> U --> W --> X --> 0 in M. We also have the dual result of the above theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-03T17:54:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "18E30"
    ],
    "keywords": [
      "auslander-reiten sequence",
      "subcategory",
      "finite dimensional algebra",
      "dual result",
      "paper studies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0633N"
    }
  }
}