{
  "id": "1709.05049",
  "version": "v1",
  "published": "2017-09-15T03:50:33.000Z",
  "updated": "2017-09-15T03:50:33.000Z",
  "title": "From support $τ$-tilting posets to algebras",
  "authors": [
    "Ryoichi Kase"
  ],
  "comment": "42 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "The aim of this paper is to study a poset isomorphism between two support $\\tau$-tilting posets. We take several algebraic information from combinatorial properties of support $\\tau$-tilting posets. As an application, we treat a certain class of basic algebras which contains preprojective algebras of type $A$, Nakayama algebras, and generalized Brauer tree algebras. We provide a necessary condition for that an algebra $\\Lambda$ share the same support $\\tau$-tilting poset with a given algebra $\\Gamma$ in this class. Furthermore, we see that this necessary condition is also a sufficient condition if $\\Gamma$ is either a preprojective algebra of type $A$, a Nakayama algebra, or a generalized Brauer tree algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T03:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "06A06",
      "16D80"
    ],
    "keywords": [
      "tilting poset",
      "generalized brauer tree algebra",
      "necessary condition",
      "nakayama algebra",
      "preprojective algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}