{
  "id": "2008.05361",
  "version": "v1",
  "published": "2020-08-11T05:40:08.000Z",
  "updated": "2020-08-11T05:40:08.000Z",
  "title": "On inner Poisson structures of a quantum cluster algebra without coefficients",
  "authors": [
    "Fang Li",
    "Jie Pan"
  ],
  "comment": "15 pages. arXiv admin note: substantial text overlap with arXiv:2003.12257",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "The main aim of this article is to characterize inner Poisson structure on a quantum cluster algebra without coefficients. Mainly, we prove that inner Poisson structure on a quantum cluster algebra without coefficients is always a standard Poisson structure. In order to relate with compatible Poisson structure, we introduce the concept of so-called locally inner Poisson structure on a quantum cluster algebra and then show it is equivalent to locally standard Poisson structure in the case without coefficients. Based on the result from \\cite{LP} we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T05:40:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "46L65",
      "17B63"
    ],
    "keywords": [
      "quantum cluster algebra",
      "coefficients",
      "locally inner poisson structure",
      "compatible poisson structure",
      "characterize inner poisson structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}