{
  "abstract": "Let $f:\\N^{k}\\to\\N^{\\ell}$ be a surjective monoid homomorphism and let $Γ$ be a row-finite $\\ell$-graph with no sources and finitely many vertices. We give an explicit graded isomorphism from the Kumjian--Pask algebra of the pullback $f^{*}Γ$ onto the tensor product of $\\KP_{\\K}(Γ)$ and the group algebra of the kernel of the group completion of $f$. When $Γ$ is strongly aperiodic, but need not be cofinal, every maximal tail $T$ and every maximal ideal $\\mathfrak m$ of the kernel group algebra determine an explicit primitive ideal and primitive quotient. If, in addition, $\\K$ is uncountable and algebraically closed, these ideals exhaust the primitive spectrum. We prove that the resulting parametrisation is a homeomorphism for the product of the maximal-tail and Zariski topologies. Each primitive ideal is realised as the annihilator of a simple module induced from the isotropy of a path which is cofinal in $T$, and the character fibres are algebraic tori. Two examples exhibit, respectively, a single character fibre and the non-Hausdorff gluing of two such fibres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20230",
  "author_total": 1,
  "authors": [
    {
      "name": "Bich Van Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0czxv23hpq7d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20230",
  "fulltext_url": null,
  "id": "e0czxv23hpq7d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20230",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213586823",
  "pdf_url": "https://arxiv.org/pdf/2609.20230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0czxv23hpq7d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Maximal tails,character fibres and induced modules for pullback Kumjian-Pask algebras",
  "title_text": "Maximal tails,character fibres and induced modules for pullback Kumjian-Pask algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/e0czxv23hpq7d",
  "venue": "arXiv",
  "versions": []
}