{
  "id": "1412.8106",
  "version": "v1",
  "published": "2014-12-28T04:39:21.000Z",
  "updated": "2014-12-28T04:39:21.000Z",
  "title": "Monoidal categorification of cluster algebras",
  "authors": [
    "Seok-Jin Kang",
    "Masaki Kashiwara",
    "Myungho Kim",
    "Se-jin Oh"
  ],
  "comment": "44 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We give a definition of monoidal categorifications of quantum cluster algebras and provide a criterion for a monoidal category of finite-dimensional graded $R$-modules to become a monoidal categorification of a quantum cluster algebra, where $R$ is a symmetric Khovanov-Lauda-Rouquier algebra. Roughly speaking, this criterion asserts that a quantum monoidal seed can be mutated successively in all the directions once the first-step mutations are possible. In the course of the study, we also give a proof of a conjecture of Leclerc on the product of upper global basis elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-28T04:39:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "81R50",
      "17B37"
    ],
    "keywords": [
      "monoidal categorification",
      "quantum cluster algebra",
      "upper global basis elements",
      "symmetric khovanov-lauda-rouquier algebra",
      "monoidal category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8106K"
    }
  }
}