{
  "abstract": "Let E be an arbitrary graph, K a field, and D the set of boundary paths of E consisting of both infinite paths and finite paths ending at singular vertices. The space KD of K-valued functions on D is a right module over the Leavitt path algebra LK(E). For a non- empty set S ? D that is strongly connected and closed under adding and deleting initial segments, we study the submodule N_S = 1_S.LK(E) generated by the indicator function of S. Let S_0 be the set of vertices lying on the paths in S. We show that N_S is simple if and only if S contains no breaking vertex of the hereditary saturated set H = E0 nS0. In particular, when S contains only infinite paths or when E is a row- finite graph, NS is a simple module. Up to isomorphism, the simple module NS depends only on S_0. When S is an infinite set of paths, the simple module NS is neither graded nor projective. The left module LK(E)1_S, obtained by twisting the action through the involution of LK(E), is simple exactly when NS is, and, when S is infinite, it is not isomorphic to any of the Chen simple modules. For the rose graph R_n with n ? 2 petals, we show that LK(R_n)1_S is isomorphic to one of the twisted Chen modules constructed by Nam, Srivastava and Vien, and to none of the other simple modules in their list. Moreover, when S is not a single vertex, the simple module NS is finitely presented if and only if only finitely many edges of E have both source and range in S_0; in particular, every simple module N_S is finitely presented when E is a finite graph. Finally, we determine when the analogous module generated by an indicator function over the Cohn path algebra CK(E) is simple. 1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08344",
  "author_total": 2,
  "authors": [
    {
      "name": "Elizabeth Pacheco"
    },
    {
      "name": "Kulumani M. Rangaswamy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ca3ga78yx9gay.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08344",
  "fulltext_url": null,
  "id": "ca3ga78yx9gay",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08344",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08344",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ca3ga78yx9gay.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08344",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08344"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Simple Modules over Leavitt Path Algebras Generated by Indicator Functions on Paths",
  "title_text": "Simple Modules over Leavitt Path Algebras Generated by Indicator Functions on Paths",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/ca3ga78yx9gay",
  "venue": "arXiv",
  "versions": []
}