{
  "abstract": "Let $(X,r)$ be a finite square-free distributive set-theoretic solution of the Yang-Baxter equation, and let $\\mathcal{A}(X,r)$ be its associated Yang-Baxter algebra. We prove that $\\mathcal{A}(X,r)$ is isomorphic to a skew polynomial algebra and explicitly compute its Nakayama automorphism. We study the natural faithful action of the permutation group $\\mathcal{G}(X,r)$ on $\\mathcal{A}(X,r)$ by graded algebra automorphisms. We characterize when $\\mathcal{G}(X,r)$ is a reflection group and, in that case, describe the invariant subalgebra $\\mathcal{A}(X,r)^{\\mathcal{G}(X,r)}$ together with its Jacobian, reflection arrangement, and discriminant. We further establish a necessary and sufficient condition for the noncommutative Auslander theorem to hold for the permutation group action on a distributive Yang-Baxter algebra. Finally, for a class of non-trivial distributive Yang-Baxter algebras, we obtain a lower bound for the pertinency of the permutation group action.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14220",
  "author_total": 2,
  "authors": [
    {
      "name": "Ji-Wei He"
    },
    {
      "name": "Xiaolan Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/710wt29sj3hqf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14220",
  "fulltext_url": null,
  "id": "710wt29sj3hqf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14220",
  "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",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213256783",
  "pdf_url": "https://arxiv.org/pdf/2609.14220",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/710wt29sj3hqf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.14220",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14220"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Yang-Baxter permutation group actions on distributive Yang-Baxter algebras",
  "title_text": "Yang-Baxter permutation group actions on distributive Yang-Baxter algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/710wt29sj3hqf",
  "venue": "arXiv",
  "versions": []
}