{
  "id": "0710.4329",
  "version": "v1",
  "published": "2007-10-23T20:10:47.000Z",
  "updated": "2007-10-23T20:10:47.000Z",
  "title": "On tilting modules over cluster-tilted algebras",
  "authors": [
    "David Smith"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category $\\mathcal{C}_H$. As a first application, we describe the induced exchange relation for tilting $A$-modules arising from the exchange relation for tilting object in $\\mathcal{C}_H$. As a second application, we exhibit tilting $A$-modules having cluster-tilted endomorphism algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-23T20:10:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "18E30"
    ],
    "keywords": [
      "cluster-tilted algebra",
      "tilting modules",
      "tilting object",
      "associated cluster category",
      "cluster-tilted endomorphism algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4329S"
    }
  }
}