{
  "id": "2412.12431",
  "version": "v1",
  "published": "2024-12-17T00:48:14.000Z",
  "updated": "2024-12-17T00:48:14.000Z",
  "title": "Finite Dimensional Representations of Quivers with Oriented Cycles",
  "authors": [
    "K. R. Goodearl",
    "B. Huisgen-Zimmermann"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $K$ be a field, $Q$ a quiver, and $\\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\\mathcal{A}^L$, $L \\in \\mathbb{N}$, tracking their development as $L$ goes to infinity. The goal is to gain a better understanding of the category of those finite dimensional $KQ$-modules which arise as finitely generated modules over admissible quotients of $KQ$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-17T00:48:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16D70",
      "16D90",
      "16G20",
      "16P10"
    ],
    "keywords": [
      "finite dimensional representations",
      "oriented cycles",
      "path algebra",
      "representation theories",
      "development"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}