{
  "abstract": "Let $p,q$ be roots of unity with $pq\\neq1$, and put $\\ell=|\\langle p,q\\rangle|$ and $t=\\ord(pq)$. Up to isomorphism, the two-parameter quantum Heisenberg algebras $\\mathcal H_{p,q}$ are exactly the noetherian PI graded down-up algebras, so everything here holds for that whole class. The ozone group is $μ_\\ell\\timesμ_{\\ell/t}$, generated by conjugation by three normal elements, and the center is recovered from the fixed ring of the ozone group as the invariants of a cyclic group of order $t$. We give a presentation of the center as a hypersurface over a cyclic quotient surface singularity. It is regular exactly when $1$ is a characteristic root, which disproves a conjecture of Chan, Gaddis, Won and Zhang, and Gorenstein exactly when $p^{m/h}=q^{n/h}$, where $m=\\ord(p)$, $n=\\ord(q)$ and $h=\\gcd(m,n)$; for $p=ζ_5$, $q=ζ_5^{2}$ it is not. We also decide when the fixed ring of the ozone group is Gorenstein and when $\\mathcal H_{p,q}$ is Calabi--Yau, and show that the algebras with regular center have non-affine automorphisms and nonzero locally nilpotent derivations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31781",
  "author_total": 3,
  "authors": [
    {
      "name": "James Gómez"
    },
    {
      "name": "Héctor Suárez"
    },
    {
      "name": "Helbert Venegas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8m6546rhqy9sy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31781",
  "fulltext_url": null,
  "id": "8m6546rhqy9sy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31781",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223695873",
  "pdf_url": "https://arxiv.org/pdf/2610.31781",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8m6546rhqy9sy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31781",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31781"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ozone groups and centers of two-parameter quantum Heisenberg algebras",
  "title_text": "Ozone groups and centers of two-parameter quantum Heisenberg algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/8m6546rhqy9sy",
  "venue": "arXiv",
  "versions": []
}