{
  "abstract": "Suppose that $r: X^2 \\to X^2$ is a nondegenerate, involutive solution to the set-theoretic Yang--Baxter equation. To this data, we can associate an Artin--Schelter regular algebra $A$ and an infinite family of groups $G_k$, where $k \\geqslant 1$. For each $k$, we show that $G_k$ is a dual reflection group for $A$, in the sense the component of $A$ graded by $1_{G_k}$ is again Artin--Schelter regular. We also show that, using the additional structure afforded by the underlying solution to the Yang--Baxter equation, one can determine the centre, Koszul complex, and associated twisted superpotential for $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26042",
  "author_total": 1,
  "authors": [
    {
      "name": "Simon Crawford"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ebnzcpps0v38k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26042",
  "fulltext_url": null,
  "id": "ebnzcpps0v38k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26042",
  "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": "W7223060268",
  "pdf_url": "https://arxiv.org/pdf/2610.26042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ebnzcpps0v38k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Dual Reflection Groups from Solutions to the Yang--Baxter Equation",
  "title_text": "Dual Reflection Groups from Solutions to the Yang--Baxter Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/ebnzcpps0v38k",
  "venue": "arXiv",
  "versions": []
}