{
  "id": "1804.04282",
  "version": "v1",
  "published": "2018-04-12T02:07:41.000Z",
  "updated": "2018-04-12T02:07:41.000Z",
  "title": "Projective objects in the category of locally finite dimensional representations of an interval finite quiver",
  "authors": [
    "Pengjie Jiao"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\\mathrm{rep}(Q)$ of locally finite dimensional representations. We show that an object in $\\mathrm{rep}(Q)$ is projective if and only if it is the direct sum of countably generated flat representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-12T02:07:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16A50",
      "18A30"
    ],
    "keywords": [
      "locally finite dimensional representations",
      "interval finite quiver",
      "direct sum",
      "countably generated flat representations",
      "indecomposable projective objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}