{
  "id": "2410.09496",
  "version": "v1",
  "published": "2024-10-12T11:22:36.000Z",
  "updated": "2024-10-12T11:22:36.000Z",
  "title": "The tensorial description of the Auslander algebras for of string algebras",
  "authors": [
    "Hui Chen",
    "Jian He",
    "Yu-Zhe Liu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The aim of this article is to study the Auslander algebra of any representation-finite string algebra. More precisely, we introduce the notion of gluing algebras and show that the Auslander algebra of a representation-finite string algebra is a quotient of a \\gluing algebra of $\\vec{A}^e_n $. As applications, the Auslander algebras of two classes of string algebras whose quivers are Dynkin types $A$ and $D$ are described. Moreover, the representation types of the above Auslander algebras are also given exactly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-12T11:22:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "auslander algebra",
      "tensorial description",
      "representation-finite string algebra",
      "representation types",
      "dynkin types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}