{
  "id": "1505.07497",
  "version": "v1",
  "published": "2015-05-27T21:44:49.000Z",
  "updated": "2015-05-27T21:44:49.000Z",
  "title": "Distributive lattices of tilting modules and support $τ$-tilting modules over path algebras",
  "authors": [
    "Yichao Yang"
  ],
  "comment": "9 pages, 6 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we study the poset of basic tilting $kQ$-modules when $Q$ is a Dynkin quiver, and the poset of basic support $\\tau$-tilting $kQ$-modules when $Q$ is a connected acyclic quiver respectively. It is shown that the first poset is a distributive lattice if and only if $Q$ is of types $\\mathbb{A}_{1}, \\mathbb{A}_{2}$ or $\\mathbb{A}_{3}$ with a nonlinear orientation and the second poset is a distributive lattice if and only if $Q$ is of type $\\mathbb{A}_{1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-27T21:44:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70",
      "05E10"
    ],
    "keywords": [
      "tilting modules",
      "distributive lattice",
      "path algebras",
      "second poset",
      "dynkin quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507497Y"
    }
  }
}