{
  "abstract": "Let $K(n)$ be the generalized Kronecker quiver, and let $(T(n),Ω)$ be the universal covering of $K(n)$, where $n\\geq 3$ and $Ω$ is a bipartite orientation. We introduce three different types of representations for quiver $(T(n),Ω)$ by $K(n)$: maps are injective in a representation maps are all surjective in a representation, and representations are of constant rank. We use $\\Inj, \\Sur$ and $\\GR$ to denote the corresponding subcategories containing these representations, respectively, and we show that \\begin{center} $\\GR= \\Inj\\cup\\Sur$. \\end{center}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14240",
  "author_total": 1,
  "authors": [
    {
      "name": "Jie Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwhy427jmmn4z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14240",
  "fulltext_url": null,
  "id": "bwhy427jmmn4z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14240",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213366663",
  "pdf_url": "https://arxiv.org/pdf/2609.14240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwhy427jmmn4z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Graded Kronecker Modules of Constant Rank",
  "title_text": "Graded Kronecker Modules of Constant Rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bwhy427jmmn4z",
  "venue": "arXiv",
  "versions": []
}