{
  "id": "1304.0667",
  "version": "v3",
  "published": "2013-04-02T15:36:35.000Z",
  "updated": "2013-12-03T11:47:37.000Z",
  "title": "Classifying τ-tilting modules over preprojective algebras of Dynkin type",
  "authors": [
    "Yuya Mizuno"
  ],
  "comment": "26 pages. Minor changes, to appear in Math. Z",
  "categories": [
    "math.RT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "We study support $\\tau$-tilting modules over preprojective algebras of Dynkin type. We classify basic support $\\tau$-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in bijection with the set of torsion classes, the set of torsion-free classes and other important objects in representation theory. We also study $g$-matrices of support $\\tau$-tilting modules, which show terms of minimal projective presentations of indecomposable direct summands. We give an explicit description of $g$-matrices and prove that cones given by $g$-matrices coincide with chambers of the associated root systems.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-03T11:47:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynkin type",
      "preprojective algebras",
      "tilting modules",
      "study support",
      "associated root systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0667M"
    }
  }
}