{
  "id": "2402.03652",
  "version": "v1",
  "published": "2024-02-06T02:56:42.000Z",
  "updated": "2024-02-06T02:56:42.000Z",
  "title": "On the Ringel--Hall algebra of the gentle one-cycle algebra $Λ(n-1,1,1)$",
  "authors": [
    "Hui Chen",
    "Dong Yang"
  ],
  "comment": "7 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "It is shown that the gentle one-cycle algebra $\\Lambda(n-1,1,1)$ has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel--Hall Lie algebra of $\\Lambda(n-1,1,1)$ is shown to be isomorphic to its Riedtmann Lie algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T02:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B37"
    ],
    "keywords": [
      "gentle one-cycle algebra",
      "ringel-hall algebra",
      "hall polynomials",
      "ringel-hall lie algebra",
      "riedtmann lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}