{
  "abstract": "In 2023, the first author, Nunez, Singh, and Swain [10] formulated an analogue of Kaplansky's idempotent conjecture for integral quandle rings. In this paper, we develop a new Fourier-analytic approach to quandle rings and use it to establish the conjecture for two major classes of quandles: Takasaki quandles, including dihedral quandles, and medial commutative quandles. A central contribution of the paper is the introduction of Fourier analysis on Alexander quandles, which provides a new framework for studying quandle rings and, in particular, their idempotents. Using this Fourier-analytic framework, we also prove that a previously known sufficient condition for the existence of counterexamples to the conjecture is in fact necessary, thereby resolving a problem of Jablonowski [12].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03799",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohamed Elhamdadi"
    },
    {
      "name": "Luc Ta"
    },
    {
      "name": "Bryce Virgin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72e076jgh3r2g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03799",
  "fulltext_url": null,
  "id": "72e076jgh3r2g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03799",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7208723682",
  "pdf_url": "https://arxiv.org/pdf/2609.03799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72e076jgh3r2g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fourier Analysis and Idempotents in Quandle Algebras",
  "title_text": "Fourier Analysis and Idempotents in Quandle Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/72e076jgh3r2g",
  "venue": "arXiv",
  "versions": []
}