{
  "id": "1608.01239",
  "version": "v1",
  "published": "2016-08-03T16:13:58.000Z",
  "updated": "2016-08-03T16:13:58.000Z",
  "title": "A new characterization of Auslander algebras",
  "authors": [
    "Shen Li",
    "Shunhua Zhang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $\\Lambda$ be a finite dimensional Auslander algebra. For a $\\Lambda$-module $M$, we prove that the projective dimension of $M$ is at most one if and only if the projective dimension of its socle soc\\,$M$ is at most one. As an application, we give a new characterization of Auslander algebra $\\Lambda$, and prove that a finite dimensional algebra $\\Lambda$ is an Auslander algebra provided its global dimension gl.d\\,$\\Lambda\\leq2$ and an injective $\\Lambda$-module is projective if and only if the projective dimension of its socle is at most one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-03T16:13:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "projective dimension",
      "finite dimensional auslander algebra",
      "finite dimensional algebra",
      "global dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}