{
  "id": "1308.0478",
  "version": "v3",
  "published": "2013-08-02T12:32:13.000Z",
  "updated": "2016-01-05T15:29:27.000Z",
  "title": "The representation type of Jacobian algebras",
  "authors": [
    "Christof Geiß",
    "Daniel Labardini-Fragoso",
    "Jan Schröer"
  ],
  "comment": "71 pages. v2: Theorem 1.4(ii) is now more general than in v1. v3: several typos fixed, references updated and not used references deleted. Exposition, mainly in Section 8.2 expanded and improved. Final version, to appear in Adv. Math",
  "doi": "10.1016/j.aim.2015.09.038",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that the representation type of the Jacobian algebra P(Q,S) associated to a 2-acyclic quiver Q with non-degenerate potential S is invariant under QP-mutations. We prove that, apart from very few exceptions, P(Q,S) is of tame representation type if and only if Q is of finite mutation type. We also show that most quivers Q of finite mutation type admit only one non-degenerate potential up to weak right equivalence. In this case, the isomorphism class of P(Q,S) depends only on Q and not on S.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-11T12:57:01.000Z",
      "comment": "67 pages. v2: Theorem 1.4(ii) is now more general than in v1",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-01-05T15:29:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobian algebra",
      "non-degenerate potential",
      "finite mutation type admit",
      "tame representation type",
      "weak right equivalence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0478G"
    }
  }
}