{
  "id": "1812.05034",
  "version": "v1",
  "published": "2018-12-12T17:10:55.000Z",
  "updated": "2018-12-12T17:10:55.000Z",
  "title": "A note on cluster automorphism groups",
  "authors": [
    "Wen Chang",
    "Ralf Schiffler"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We conjecture a characterization of a cluster automorphism as an algebra homomorphism from the cluster algebra to itself that restricts to a bijection between two clusters. This formulation does not require that the map commutes with mutations as in the original definition of cluster automorphisms. We prove the conjecture in the case where at least one of the two clusters is bipartite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-12T17:10:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60"
    ],
    "keywords": [
      "cluster automorphism groups",
      "conjecture",
      "original definition",
      "algebra homomorphism",
      "map commutes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}