{
  "id": "2105.09636",
  "version": "v1",
  "published": "2021-05-20T10:06:58.000Z",
  "updated": "2021-05-20T10:06:58.000Z",
  "title": "Gluing support $τ$-tilting modules via symmetric ladders of height 2",
  "authors": [
    "Yingying Zhang"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Recent result by Adachi-Iyama-Reiten has shown a bijective correspondence between support $\\tau$-tilting modules and functorially finite torsion classes. On the other hand, the techniques of gluing torsion classes along a recollement were investigated by Liu-Vit\\'oria-Yang and Ma-Huang. In this article, we show that gluing torsion classes can be restricted to functorially finiteness condition in the symmetric ladders of height 2. Then using the above correspondence with support $\\tau$-tilting modules, we present explicit constructions of gluing of support $\\tau$-tilting modules via symmetric ladders of height 2. Finally, we apply the results to triangular matrix algebras to give a more detailed version of the known Jasso's reduction and study maximal green sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-20T10:06:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16S50",
      "18A40",
      "18E10"
    ],
    "keywords": [
      "tilting modules",
      "symmetric ladders",
      "gluing support",
      "gluing torsion classes",
      "study maximal green sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}