{
  "id": "2006.12684",
  "version": "v1",
  "published": "2020-06-23T01:09:24.000Z",
  "updated": "2020-06-23T01:09:24.000Z",
  "title": "On the radical of Cluster tilted algebras",
  "authors": [
    "Claudia Chaio",
    "Victoria Guazzelli"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We determine the minimal lower bound $n$, with $n \\geq 1$, where the $n$-th power of the radical of the module category of a representation-finite cluster tilted algebra vanishes. We give such a bound in terms of the number of vertices of the underline quiver. Consequently, we get the nilpotency index of the radical of the module category for representation-finite self-injective cluster tilted algebras. We also study the non-zero composition of $m$, $m \\ge 2$, irreducible morphisms between indecomposable modules in representation-finite cluster tilted algebras lying in the $(m+1)$-th power of the radical of their module category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-23T01:09:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "module category",
      "cluster tilted algebras lying",
      "representation-finite cluster tilted algebra vanishes",
      "th power",
      "minimal lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}