{
  "abstract": "The Lie algebra of multiple zeta values is realized as the space $\\operatorname{ARI}^{\\operatorname{pol}}_{\\underline{al}\\ast \\underline{il}}$ of alternal moulds whose swap is alternil up to a constant mould, equipped with the $ari$ bracket. In this paper, we study the larger space $\\operatorname{BARI}_{\\underline{il},swap}^{\\operatorname{pol}}$ of alternil, swap-invariant bimoulds, which is conjecturally the Lie algebra for multiple $q$-zeta values. We propose an explicit formula for a Lie bracket $uri$ on this space. Moreover, we prove that the Lie algebra $\\operatorname{ARI}^{\\operatorname{pol}}_{\\underline{al}\\ast \\underline{il}}$ embeds into $\\operatorname{BARI}_{\\underline{il},swap}^{\\operatorname{pol}}$, with the $ari$ bracket translating directly into the $uri$ bracket. Finally, we examine the associated-depth graded of $\\operatorname{BARI}_{\\underline{il},swap}^{\\operatorname{pol}}$, extending the known depth-graded setup for $\\operatorname{ARI}_{\\underline{al}\\ast \\underline{il}}^{\\operatorname{pol}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25168",
  "author_total": 3,
  "authors": [
    {
      "name": "Annika Burmester"
    },
    {
      "name": "Ulf Kühn"
    },
    {
      "name": "Leila Schneps"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nfd12dvfbtza.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25168",
  "fulltext_url": null,
  "id": "3nfd12dvfbtza",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25168",
  "language": "en",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25168",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nfd12dvfbtza.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25168",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25168"
    },
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05848048",
      "source": "hal",
      "url": "https://hal.science/hal-05848048v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Moulds, Bimoulds, and some Lie algebras",
  "title_text": "Moulds, Bimoulds, and some Lie algebras",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:48Z",
  "url": "https://research.draconitic.com/paper/3nfd12dvfbtza",
  "venue": "arXiv",
  "versions": []
}