{
  "id": "1302.2709",
  "version": "v4",
  "published": "2013-02-12T06:15:58.000Z",
  "updated": "2014-03-27T01:14:15.000Z",
  "title": "Reduction of $τ$-tilting modules and torsion pairs",
  "authors": [
    "Gustavo Jasso"
  ],
  "comment": "32 pages. Shortened abstract, corrected typos in references [1] and [9]",
  "categories": [
    "math.RT"
  ],
  "abstract": "The class of support $\\tau$-tilting modules was introduced recently by Adachi, Iyama and Reiten. These modules complete the class of tilting modules from the point of view of mutations. Given a finite dimensional algebra $A$, we study all basic support $\\tau$-tilting $A$-modules which have given basic $\\tau$-rigid $A$-module as a direct summand. We show that there exist an algebra $C$ such that there exists an order-preserving bijection between these modules and all basic support $\\tau$-tilting $C$-modules; we call this process $\\tau$-tilting reduction. An important step in this process is the formation of $\\tau$-perpendicular categories which are analogs of ordinary perpendicular categories. Finally, we show that $\\tau$-tilting reduction is compatible with silting reduction and 2-Calabi-Yau reduction in appropiate triangulated categories.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-03-27T01:14:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10"
    ],
    "keywords": [
      "tilting modules",
      "torsion pairs",
      "basic support",
      "finite dimensional algebra",
      "tilting reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.2709J"
    }
  }
}