{
  "id": "1801.04312",
  "version": "v1",
  "published": "2018-01-12T20:52:01.000Z",
  "updated": "2018-01-12T20:52:01.000Z",
  "title": "A characterisation of $τ$-tilting finite algebras",
  "authors": [
    "Lidia Angeleri Hügel",
    "Frederik Marks",
    "Jorge Vitória"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We prove that a finite dimensional algebra is $\\tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $\\tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of basic support $\\tau$-tilting (that is, finite dimensional silting) modules and equivalence classes of ring epimorphisms $A\\longrightarrow B$ with ${\\rm Tor}_1^A(B,B)=0$. It follows that a finite dimensional algebra is $\\tau$-tilting finite if and only if there are only finitely many equivalence classes of such ring epimorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-12T20:52:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16S85",
      "16S90"
    ],
    "keywords": [
      "tilting finite algebra",
      "finite dimensional algebra",
      "equivalence classes",
      "characterisation",
      "admit large silting modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}