{
  "id": "1904.11903",
  "version": "v1",
  "published": "2019-04-26T15:43:57.000Z",
  "updated": "2019-04-26T15:43:57.000Z",
  "title": "Stratifying systems through $τ$-tilting theory",
  "authors": [
    "Octavio Mendoza",
    "Hipolito Treffinger"
  ],
  "comment": "20 pages. Commentaries are welcome",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper we study the stratifying systems, introduced by K. Erdmann and C. Saenz in \\cite{Erdmann2003}, by using the $\\tau$-tilting theory introduced by T. Adachi, O. Iyama and I. Reiten in \\cite{AIR}. We give a constructive proof that every non-zero $\\tau$-rigid module induces at least one stratifying system for any finite dimensional algebra $A$. Later, we show that each stratifying system found this way is a $\\tau$-exceptional sequence as defined by A. B. Buan and R. Marsh in \\cite{BM}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-26T15:43:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stratifying system",
      "tilting theory",
      "rigid module induces",
      "finite dimensional algebra",
      "exceptional sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}