{
  "id": "1610.05458",
  "version": "v1",
  "published": "2016-10-18T07:07:34.000Z",
  "updated": "2016-10-18T07:07:34.000Z",
  "title": "An introduction to higher Auslander-Reiten theory",
  "authors": [
    "Gustavo Jasso",
    "Sondre Kvamme"
  ],
  "comment": "27 pages, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "This article consists of an introduction to Iyama's higher Auslander-Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander-Reiten theory, including the existence of $d$-almost-split sequences in $d$-cluster-tilting subcategories, following the approach to classical Auslander-Reiten theory due to Auslander, Reiten, and Smal{\\o}. We show that Krause's proof of Auslander's defect formula can be adapted to give a new proof of the defect formula for $d$-exact sequences. We use the defect formula to establish the existence of morphisms determined by objects in $d$-cluster-tilting subcategories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-18T07:07:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "16G10"
    ],
    "keywords": [
      "introduction",
      "iyamas higher auslander-reiten theory",
      "cluster-tilting subcategories",
      "auslanders defect formula",
      "exact sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}