{
  "id": "2211.12984",
  "version": "v1",
  "published": "2022-11-23T14:42:32.000Z",
  "updated": "2022-11-23T14:42:32.000Z",
  "title": "Decompositions of Infinite-Dimensional $A_{ \\infty,\\infty}$ Quiver Representations",
  "authors": [
    "Nathaniel Gallup",
    "Stephen Sawin"
  ],
  "comment": "21 page, 2 figures",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph $A_{\\infty, \\infty}$ is Krull-Schmidt, as long as the arrows in the quiver eventually point outward.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-23T14:42:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20"
    ],
    "keywords": [
      "quiver representations",
      "decompositions",
      "linear algebraic methods",
      "krull-schmidt"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}