{
  "abstract": "Let \\(R\\) be any unital ring equipped with a Sylvester matrix rank function, and let \\(Q\\) be the rank completion of the matrix system defined by block-diagonal embeddings along a factor sequence. We prove that both \\(\\GL(Q)\\) and \\((Q,+)\\) are exotic: every strongly continuous unitary representation is trivial. We also prove that \\(\\GL(Q)\\) is Bourbaki bounded and admits no nonzero escape function. For every \\(\\varepsilon>0\\), let \\(B_\\varepsilon\\) be the open ball centered at the identity. The least positive integer \\(N\\) such that \\(\\GL(Q)=B_\\varepsilon^N\\) is \\(\\lfloor\\varepsilon^{-1}\\rfloor+1\\). Neither regularity nor irreducibility is required. Our proof of exoticness uses a uniform Kazhdan estimate for additive integer matrix groups together with rank-one matrix perturbations, rather than the character-theoretic and continuous ring methods used previously. The geometric conclusions follow from factorizations using diagonal corner subgroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24212",
  "author_total": 1,
  "authors": [
    {
      "name": "Baojie Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abtvae0v175g9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24212",
  "fulltext_url": null,
  "id": "abtvae0v175g9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24212",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214034059",
  "pdf_url": "https://arxiv.org/pdf/2609.24212",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abtvae0v175g9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24212",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24212"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exotic Unit Groups of Sylvester Rank Completions",
  "title_text": "Exotic Unit Groups of Sylvester Rank Completions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/abtvae0v175g9",
  "venue": "arXiv",
  "versions": []
}