{
  "abstract": "Let $R=L_{\\F_2}(1,2)$. We prove that $\\GL_r(R)$ is integrally acyclic for every $r\\geq1$ and that the canonical map $\\St_r(R)\\to\\GL_r(R)$ is an isomorphism for every $r\\geq3$. The unit group $R^\\times$ is finitely presented, and we describe an explicit finite presentation. The homology calculation uses leaf coordinates, simultaneous extensions of ordered frames, and finite-field actions on stabilizers. The Steinberg argument lifts relations from a simply connected frame complex and refines coordinates. We also state separate criteria for the two arguments over rings of characteristic two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08428",
  "author_total": 1,
  "authors": [
    {
      "name": "Huynh Viet Khanh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21qg6419sj9tr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08428",
  "fulltext_url": null,
  "id": "21qg6419sj9tr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08428",
  "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.GR"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7211995135",
  "pdf_url": "https://arxiv.org/pdf/2609.08428",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21qg6419sj9tr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.08428",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08428"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "General linear and Steinberg groups over the Leavitt algebra $L_{\\mathbb F_2}(1,2)$",
  "title_text": "General linear and Steinberg groups over the Leavitt algebra L_𝔽_2(1,2)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/21qg6419sj9tr",
  "venue": "arXiv",
  "versions": []
}