{
  "abstract": "Let $R$ be a compact discrete valuation ring and $G = R^d \\rtimes \\operatorname{GL}_d(R)$. We show that the central Fourier algebra $\\operatorname{ZA}(G)$ is not amenable, reaffirming a conjecture of Alaghmandan and Spronk. Our methods reduce to studying the Fourier algebra of the commutative orbit hypergroup $H = R^d/\\operatorname{GL}_d(R)$. Along the way, we also show that dual of any commutative orbit hypergroup $H$ is the hypergroup of the corresponding dual action, and this in turn shows that $\\operatorname{A}(H) \\cong \\operatorname{L}^1(\\widehat{H})$, which aligns with the classical setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35740",
  "author_total": 1,
  "authors": [
    {
      "name": "Aleksa Vujičić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cj605ajty240.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35740",
  "fulltext_url": null,
  "id": "2cj605ajty240",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35740",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214802592",
  "pdf_url": "https://arxiv.org/pdf/2609.35740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cj605ajty240.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35740"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Fourier Algebra of Certain Compact Orbit Hypergroups",
  "title_text": "The Fourier Algebra of Certain Compact Orbit Hypergroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2cj605ajty240",
  "venue": "arXiv",
  "versions": []
}