{
  "id": "0904.3291",
  "version": "v1",
  "published": "2009-04-21T17:05:02.000Z",
  "updated": "2009-04-21T17:05:02.000Z",
  "title": "F-polynomials in Quantum Cluster Algebras",
  "authors": [
    "Thao Tran"
  ],
  "comment": "36 pages, 1 figure",
  "categories": [
    "math.RA",
    "math.CO",
    "math.RT"
  ],
  "abstract": "F-polynomials and g-vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of the initial cluster data. A quantum cluster algebra is a certain noncommutative deformation of a cluster algebra. In this paper, we define and prove the existence of analogous quantum F-polynomials for quantum cluster algebras. We prove some properties of quantum F-polynomials. In particular, we give a recurrence relation which can be used to compute them. Finally, we compute quantum F-polynomials and g-vectors for a certain class of cluster variables, which includes all cluster variables in type A quantum cluster algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-21T17:05:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "05E15",
      "20G42"
    ],
    "keywords": [
      "quantum cluster algebra",
      "expresses cluster variables",
      "initial cluster data",
      "analogous quantum f-polynomials",
      "recurrence relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.3291T"
    }
  }
}