{
  "abstract": "The classical ADE classification implies that $E_8$ is the unique irreducible unimodular Euclidean lattice generated by vectors of norm $2$. In sharp contrast, for every positive integer $m$, we construct an irreducible odd unimodular lattice of rank $24m$ and minimum norm $3$ that is generated by its minimal vectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31478",
  "author_total": 4,
  "authors": [
    {
      "name": "Hong-Jun Ge"
    },
    {
      "name": "Jack H. Koolen"
    },
    {
      "name": "Jing-Yuan Liu"
    },
    {
      "name": "Kiyoto Yoshino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rt9fknbwa1fa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31478",
  "fulltext_url": null,
  "id": "5rt9fknbwa1fa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31478",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214642742",
  "pdf_url": "https://arxiv.org/pdf/2609.31478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rt9fknbwa1fa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Irreducible rootless unimodular lattices generated by vectors of norm $3$",
  "title_text": "Irreducible rootless unimodular lattices generated by vectors of norm $3$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5rt9fknbwa1fa",
  "venue": "arXiv",
  "versions": []
}