{
  "abstract": "We prove that a Hopf algebra over an arbitrary field has a bijective antipode if either its left or right regular module has finite uniform dimension. In particular, this solves Skryabin's conjecture, posed in 2006, that every noetherian Hopf algebra has a bijective antipode. Starting from Skryabin's injectivity theorem for weakly finite Hopf algebras, we associate to each finite-dimensional subcoalgebra an essential left ideal of common denominators that is also a right coideal in the antipode image. An annihilator identity makes this image essential in the original algebra as a left module over the image, yielding finite left uniform dimension from finite right uniform dimension. A second denominator construction inside the antipode image, together with a restricted inverse-antipode identity, proves surjectivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15473",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Sciandra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11wevyfym38ya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15473",
  "fulltext_url": null,
  "id": "11wevyfym38ya",
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  "landing_url": "https://arxiv.org/abs/2610.15473",
  "language": null,
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  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
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    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  "openalex": "W7221801587",
  "pdf_url": "https://arxiv.org/pdf/2610.15473",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11wevyfym38ya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15473",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15473"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A noetherian Hopf algebra has bijective antipode",
  "title_text": "A noetherian Hopf algebra has bijective antipode",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/11wevyfym38ya",
  "venue": "arXiv",
  "versions": []
}