{
  "abstract": "We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degenerate case. We use this characterisation to show several novel examples of such structures, providing a complete classification for non-degenerate four-dimensional differential-geometric Poisson brackets under the additional assumption of the Lie algebra to be of quasi-Frobenius type. We also present a complete classification of quasi-Frobenius filiform N-graded Lie algebras, including two families in arbitrary dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40049",
  "author_total": 3,
  "authors": [
    {
      "name": "Marta Dell'Atti"
    },
    {
      "name": "Giorgio Gubbiotti"
    },
    {
      "name": "Pierandrea Vergallo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbzv5w5nqvcs6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40049",
  "fulltext_url": null,
  "id": "fbzv5w5nqvcs6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40049",
  "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-ph"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  ],
  "openalex": "W7215121555",
  "pdf_url": "https://arxiv.org/pdf/2609.40049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbzv5w5nqvcs6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Discrete differential-geometric Poisson brackets: general theory and explicit constructions",
  "title_text": "Discrete differential-geometric Poisson brackets: general theory and explicit constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/fbzv5w5nqvcs6",
  "venue": "arXiv",
  "versions": []
}