{
  "id": "2109.01248",
  "version": "v1",
  "published": "2021-09-02T23:49:06.000Z",
  "updated": "2021-09-02T23:49:06.000Z",
  "title": "A Bijection theorem for Gorenstein projective τ-tilting modules",
  "authors": [
    "Zongzhen Xie",
    "Xiaojin Zhang"
  ],
  "comment": "10 pages. Comments are welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we introduce the notions of Gorenstein projective $\\tau$-rigid modules, Gorenstein projective support $\\tau$-tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi-Iyama-Reiten's bijection theorem on support $\\tau$-tilting modules. More precisely, for an algebra $\\Lambda$, we show that there is a bijection between the set of Gorenstein projective $\\tau$-rigid pairs in $\\mod \\Lambda$ and the set of Gorenstein injective $\\tau^{-1}$-rigid pairs in $\\mod \\Lambda^{\\rm op}$. We prove that there is a bijection between the set of Gorenstein projective support $\\tau$-tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM-$\\tau$-tilting finite algebras and show that $\\Lambda$ is CM-$\\tau$-tilting finite if and only if $\\Lambda^{\\rm {op}}$ is CM-$\\tau$-tilting finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-02T23:49:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18G25"
    ],
    "keywords": [
      "tilting finite",
      "tilting modules",
      "gorenstein projective support",
      "finite gorenstein projective torsion classes",
      "rigid pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}