{
  "id": "1601.03988",
  "version": "v1",
  "published": "2016-01-15T16:28:11.000Z",
  "updated": "2016-01-15T16:28:11.000Z",
  "title": "On syzygies over 2-Calabi-Yau tilted algebras",
  "authors": [
    "Ana Garcia Elsener",
    "Ralf Schiffler"
  ],
  "comment": "22 pages, 18 figures",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We characterize the syzygies and co-syzygies over 2-Calabi-Yau tilted algebras in terms of the Auslander-Reiten translation and the syzygy functor. We explore connections between the category of syzygies, the category of Cohen-Macaulay modules, the representation dimension of algebras and the Igusa-Todorov functions. In particular, we prove that the Igusa-Todorov dimensions of d-Gorenstein algebras are equal to d. For cluster-tilted algebras of Dynkin type D, we give a geometric description of the stable Cohen-Macaulay category in terms of tagged arcs in the punctured disc. We also describe the action of the syzygy functor in a geometric way. This description allows us to compute the Auslander-Reiten quiver of the stable Cohen-Macaulay category using tagged arcs and geometric moves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-15T16:28:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G50",
      "16G70",
      "13F60"
    ],
    "keywords": [
      "tilted algebras",
      "stable cohen-macaulay category",
      "syzygy functor",
      "tagged arcs",
      "cohen-macaulay modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103988G"
    }
  }
}