{
  "id": "2111.09555",
  "version": "v2",
  "published": "2021-11-18T07:20:16.000Z",
  "updated": "2021-12-05T15:29:49.000Z",
  "title": "Dilogarithm identities in cluster scattering diagrams",
  "authors": [
    "Tomoki Nakanishi"
  ],
  "comment": "v1: 20 pp; v2: 20pp, minor changes in Sec 2.1",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We extend the notion of $y$-variables (coefficients) in cluster algebras to cluster scattering diagrams. Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a cluster scattering diagram. We show that these identities are constructed from and reduced to a trivial one by applying the pentagon identity possibly infinitely many times.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-12-05T15:29:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster scattering diagram",
      "dilogarithm identity",
      "cluster algebras",
      "coefficients",
      "pentagon identity possibly"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}