{
  "abstract": "We characterize non-commutative polynomials of degree 2 which preserve free infinite divisibility as self-adjoint Lie polynomials of degree 2. This extends previous results which characterized homogeneous quadratic forms only. The proof is based on an involution of colored noncrossing partitions cancelling many terms; positive definiteness of the remaining terms is established by an explicit operator model on Fock space. Examples show that higher order Lie polynomials do not preserve free infinite divisibility.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15320",
  "author_total": 4,
  "authors": [
    {
      "name": "Wiktor Ejsmont"
    },
    {
      "name": "Franz Lehner"
    },
    {
      "name": "Mihai Popa"
    },
    {
      "name": "Kamil Szpojankowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8144j9p31kj6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15320",
  "fulltext_url": null,
  "id": "8144j9p31kj6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15320",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221834829",
  "pdf_url": "https://arxiv.org/pdf/2610.15320",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8144j9p31kj6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15320",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15320"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Quadratic polynomials preserving free infinite divisibility",
  "title_text": "Quadratic polynomials preserving free infinite divisibility",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8144j9p31kj6w",
  "venue": "arXiv",
  "versions": []
}