{
  "id": "2406.16011",
  "version": "v1",
  "published": "2024-06-23T04:58:55.000Z",
  "updated": "2024-06-23T04:58:55.000Z",
  "title": "The derived dimensions and representation distances of artin algebras",
  "authors": [
    "Junling Zheng",
    "Yingying Zhang",
    "Jinbi Zhang"
  ],
  "comment": "accepted for publication in Archiv der Mathematik",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give a method for constructing $(m,n)$-Igusa-Todorov algebras. As an application, we present for general artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-23T04:58:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G20",
      "16E10",
      "18E10"
    ],
    "keywords": [
      "derived dimension",
      "representation distance",
      "igusa-todorov algebras",
      "general artin algebras",
      "finitistic dimension conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}