{
  "id": "2406.03370",
  "version": "v1",
  "published": "2024-06-05T15:24:44.000Z",
  "updated": "2024-06-05T15:24:44.000Z",
  "title": "A representation embedding for algebras of infinite type",
  "authors": [
    "Raymundo Bautista Ramos",
    "Jesús Efrén Pérez Terrazas",
    "Leonardo Salmerón Castro"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that for any finite-dimensional algebra $\\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\\Gamma$ and a representation embedding from $\\Gamma -$mod into $\\Lambda -$mod. As an application, we prove a variation of the Brauer-Trall Conjecture II: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T15:24:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G60",
      "16G20"
    ],
    "keywords": [
      "infinite type",
      "representation embedding",
      "infinite-representation type admit infinite families",
      "finite-dimensional algebra",
      "bounded principal ideal domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}