{
  "abstract": "We consider the problem of computing rational invariants of nilpotent Lie algebras. We compare two methods that are commonly used for this task: the method of integral curves and the Dixmier map. Given a derivation of a rational function field with polynomial coefficients, we formulate a condition under which the kernel can be recovered from a family of rational integral curves, and we show that triangular derivations satisfy this hypothesis. This yields an explicit description of the kernel as a purely transcendental extension and produces algebraically independent generators. We also show that, in the triangular case, the resulting generators agree with those obtained from the Dixmier map via a local slice. A careful analysis of the generating set obtained from this method leads to an algorithm for computing generators of the rational invariant field of a nilpotent Lie algebra. An implementation of the methods is available in the SageMath system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10956",
  "author_total": 2,
  "authors": [
    {
      "name": "Csaba Schneider"
    },
    {
      "name": "Igor Martins Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frbgjmvrgtysg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10956",
  "fulltext_url": null,
  "id": "frbgjmvrgtysg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10956",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7212291144",
  "pdf_url": "https://arxiv.org/pdf/2609.10956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frbgjmvrgtysg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10956"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Invariants of Nilpotent Lie Algebras via Geometry and Algebra with a Focus on Computation",
  "title_text": "Invariants of Nilpotent Lie Algebras via Geometry and Algebra with a Focus on Computation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/frbgjmvrgtysg",
  "venue": "arXiv",
  "versions": []
}