{
  "id": "1802.02773",
  "version": "v1",
  "published": "2018-02-08T09:50:12.000Z",
  "updated": "2018-02-08T09:50:12.000Z",
  "title": "The structure and homological properties of generalized standard Auslander-Reiten components",
  "authors": [
    "Piotr Malicki",
    "Andrzej Skowroński"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe the structure and homological properties of arbitrary generalized standard Auslander-Reiten components of artin algebras. In particular, we prove that for all but finitely many indecomposable modules in such components the Euler characteristic is defined and nonnegative. Further, we provide a handy criterion for an infinite Auslander-Reiten component of an artin algebra to be generalized standard. We solve also the long standing open problem concerning the structure of artin algebras admitting a~separating family of Auslander-Reiten components.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-08T09:50:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E10",
      "16E30",
      "16G10",
      "16G60",
      "16G70"
    ],
    "keywords": [
      "homological properties",
      "artin algebra",
      "standing open problem concerning",
      "arbitrary generalized standard auslander-reiten components",
      "infinite auslander-reiten component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}