{
  "id": "1503.04639",
  "version": "v1",
  "published": "2015-03-16T13:35:02.000Z",
  "updated": "2015-03-16T13:35:02.000Z",
  "title": "Torsion classes, wide subcategories and localisations",
  "authors": [
    "Frederik Marks",
    "Jan Stovicek"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "For a finite dimensional algebra $A$, we establish correspondences between torsion classes and wide subcategories in $mod(A)$. In case $A$ is representation finite, we obtain an explicit bijection between these two classes of subcategories. Moreover, we translate our results to the language of ring epimorphisms and universal localisations. It turns out that universal localisations over representation finite algebras are classified by torsion classes and support $\\tau$-tilting modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-16T13:35:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16S85",
      "18E40"
    ],
    "keywords": [
      "torsion classes",
      "wide subcategories",
      "universal localisations",
      "finite dimensional algebra",
      "representation finite algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}