{
  "abstract": "We obtain presentations of Borel subgroups of certain Chevalley groups and Kac-Moody groups of simply laced type. More precisely, we show that Borel subgroups of simply laced Chevalley groups over a commutative, unital ring (satisfying a minor technical condition), are the amalgamated product of their rank 2 subgroups, generalising a result of Tits over fields (different from $\\mathbb{F}_2$). We moreover show that Borel subgroups of Kac-Moody groups over local Bézout domains also have a presentation as an amalgamated product of their rank 2 subgroups as soon as this holds for their rank 3 subgroups. In particular we deduce that Borel subgroups of simply laced Kac-Moody groups over a local Bézout domain (with residue field different from $\\mathbb{F}_2$) have such a presentation if and only if they are of 3-spherical type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05224",
  "author_total": 1,
  "authors": [
    {
      "name": "Robynn Corveleyn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19b241606cax5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05224",
  "fulltext_url": null,
  "id": "19b241606cax5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05224",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220727408",
  "pdf_url": "https://arxiv.org/pdf/2610.05224",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19b241606cax5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05224",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05224"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Presentation of Borel subgroups of Kac-Moody groups over local rings",
  "title_text": "Presentation of Borel subgroups of Kac-Moody groups over local rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/19b241606cax5",
  "venue": "arXiv",
  "versions": []
}