{
  "id": "1201.6422",
  "version": "v3",
  "published": "2012-01-31T02:48:30.000Z",
  "updated": "2013-07-10T20:36:08.000Z",
  "title": "Module varieties and representation type of finite-dimensional algebras",
  "authors": [
    "Calin Chindris",
    "Ryan Kinser",
    "Jerzy Weyman"
  ],
  "comment": "14 pp., comments welcome. v3: completely revised and simplified",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we seek geometric and invariant-theoretic characterizations of (Schur-)representation finite algebras. To this end, we introduce two classes of finite-dimensional algebras: those with the dense-orbit property and those with the multiplicity-free property. We show first that when a connected algebra A admits a preprojective component, each of these properties is equivalent to A being representation-finite. Next, we give an example of an algebra which is not representation-finite but still has the dense-orbit property. We also show that the string algebras with the dense orbit-property are precisely the representation-finite ones. Finally, we show that a tame algebra has the multiplicity-free property if and only if it is Schur-representation-finite.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-10T20:36:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite-dimensional algebras",
      "module varieties",
      "representation type",
      "multiplicity-free property",
      "dense-orbit property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.6422C"
    }
  }
}