{
  "id": "1911.09021",
  "version": "v1",
  "published": "2019-11-20T16:48:47.000Z",
  "updated": "2019-11-20T16:48:47.000Z",
  "title": "On band modules and $τ$-tilting finiteness",
  "authors": [
    "Sibylle Schroll",
    "Hipolito Treffinger",
    "Yadira Valdivieso"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper we study general properties of band modules and their endomorphisms in the module category of a finite dimensional algebra. As an application we describe properties of torsion classes containing band modules. Furthermore, we show that a special biserial algebra is $\\tau$-tilting finite if and only if no band module is a brick.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-20T16:48:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting finiteness",
      "torsion classes containing band modules",
      "finite dimensional algebra",
      "special biserial algebra",
      "study general properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}