{
  "id": "2501.05045",
  "version": "v1",
  "published": "2025-01-09T08:11:25.000Z",
  "updated": "2025-01-09T08:11:25.000Z",
  "title": "Frobenius--Perron dimension via $τ$-tilting theory",
  "authors": [
    "Takahide Adachi",
    "Ryoichi Kase"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "From the viewpoint of $\\tau$-tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of $\\tau$-tilting finite algebras by a combinatorial method in $\\tau$-tilting theory. Secondly, we give the upper bound of the Frobenius--Perron dimension for a $\\tau$-tilting finite algebra of tame representation type. Thirdly, we determine the Frobenius--Perron dimensions of Nakayama algebras and generalized preprojective algebras of Dynkin type in the sense of Geiss--Leclerc--Schr\\\"oer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-09T08:11:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting theory",
      "tilting finite algebra",
      "study frobenius-perron dimensions",
      "tame representation type",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}