{
  "id": "1410.1403",
  "version": "v1",
  "published": "2014-10-06T15:00:32.000Z",
  "updated": "2014-10-06T15:00:32.000Z",
  "title": "Quivers with relations for symmetrizable Cartan matrices",
  "authors": [
    "Christof Geiss",
    "Bernard Leclerc",
    "Jan Schröer"
  ],
  "comment": "66 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce and study a class of Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path algebras of quivers associated with symmetric Cartan matrices. We also define a corresponding class of generalized preprojective algebras. Without any assumption on the ground field, we obtain new representation-theoretic realizations of all finite root systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-06T15:00:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetrizable cartan matrices",
      "finite root systems",
      "symmetric cartan matrices",
      "path algebras",
      "ground field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.1403G"
    }
  }
}