{
  "id": "1607.02473",
  "version": "v1",
  "published": "2016-07-08T17:54:14.000Z",
  "updated": "2016-07-08T17:54:14.000Z",
  "title": "$τ$-Tilting Theory and $τ$-Slices",
  "authors": [
    "Hipolito Treffinger"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Comparing the module categories of an algebra and of the endomorphism algebra of a given support $\\tau$-tilting module, we give a generalization of the Brenner-Butler's tilting theorem in the framework of $\\tau$-tilting theory. Afterwards we define $\\tau$-slices and prove that complete slices of tilted algebras and local slices of cluster tilted algebras are examples of complete $\\tau$-slices. Then we apply this concept to the study of simply connected tilted algebras. Finally, we study the one-point extensions and the split-by-nilpotent extensions of an algebra with $\\tau$-slices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-08T17:54:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting theory",
      "split-by-nilpotent extensions",
      "one-point extensions",
      "endomorphism algebra",
      "cluster tilted algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}