{
  "abstract": "Let $q$ be a primitive $n$-th root of unity, $n>1$, and let $f$ be a nonzero polynomial such that $n\\nmid(j+1)$ for every $j\\in\\supp(f)$. Set $e=\\gcd(n,\\{j+1:j\\in\\supp(f)\\})$. We show that $\\Oz(B_q(f))\\congμ_e\\timesμ_e$: the defining relations are homogeneous for a $\\mathbb{Z}/e\\times\\mathbb{Z}/e$ grading, the center sits in degree zero, and the ozone group is the character group of that grading. The determination of the ozone group only requires the central elements $u^n$, $v^n$, and $Ω$. The regular normal elements modulo the center form the same group, generated by $u^{n/e}$ and $v^{n/e}$, so every normal element is central exactly when $e=1$. For $f=t^2$ we recover a computation of Chan, Gaddis, Won and Zhang, and for $e>1$ we obtain an infinite family of Calabi--Yau algebras with nontrivial ozone group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28868",
  "author_total": 2,
  "authors": [
    {
      "name": "James Gómez"
    },
    {
      "name": "Helbert Venegas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bfc797k7dpdx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28868",
  "fulltext_url": null,
  "id": "8bfc797k7dpdx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28868",
  "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.RA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204929179",
  "pdf_url": "https://arxiv.org/pdf/2608.28868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bfc797k7dpdx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28868"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The ozone groups of the algebras $B_q(f)$",
  "title_text": "The ozone groups of the algebras B_q(f)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8bfc797k7dpdx",
  "venue": "arXiv",
  "versions": []
}