{
  "abstract": "In this paper, we complete the classification of 4×4 4 × 4 analytic solutions of the Yang–Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang–Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R R -matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R R -matrices satisfy a modified Yang–Baxter equation instead.",
  "abstract_shown": true,
  "affiliations": [
    "Trinity College Dublin"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Marius de Leeuw",
      "orcid": "0000-0002-4578-5062"
    },
    {
      "affs": [
        0
      ],
      "name": "Vera Posch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bk7yvr9azg8pd.bib",
  "cited_by": 10,
  "doi": "10.21468/scipostphys.21.3.060",
  "fulltext_url": null,
  "id": "bk7yvr9azg8pd",
  "issns": [
    "2542-4653"
  ],
  "landing_url": "https://doi.org/10.21468/scipostphys.21.3.060",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212161531",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": "SciPost.org",
  "ris": "https://research.draconitic.com/paper/bk7yvr9azg8pd.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W7212161531",
      "source": "openalex",
      "url": "https://doi.org/10.21468/scipostphys.21.3.060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Solving the $4 \\times 4$ quantum Yang-Baxter equation",
  "title_text": "Solving the 4 × 4 quantum Yang-Baxter equation",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/bk7yvr9azg8pd",
  "venue": "SciPost Physics",
  "versions": []
}