{
  "abstract": "A Kähler structure on a real Lie algebra $\\mathfrak{g}$ is a pair $(ω, J)$ of a 2-cocycle and a complex structure on $\\mathfrak{g}$ which are compatible in the sense that $J$ is skew-symmetric with respect to $ω$. This paper investigates Kähler structures on Lie algebras, with a particular focus on the nilpotent case. We introduce an algebraic framework for the Kählerian reduction and oxidation of Lie algebras by one-dimensional and two-dimensional ideals. Our main structural result demonstrates that every indecomposable, quasi-nilpotent Kählerian nilpotent Lie algebra of dimension greater than four can be inductively reconstructed through a finite sequence of Kählerian central oxidations by planes. This reduction sequence originates from a base algebra that is either $\\{0\\}$, $\\mathbb{R}^2$, or one admitting a strongly non-nilpotent complex structure. Moreover, if the complex structure is nilpotent, all intermediate reductions also have a nilpotent complex structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26417",
  "author_total": 3,
  "authors": [
    {
      "name": "Mustapha Bachaou"
    },
    {
      "name": "Ignacio Bajo"
    },
    {
      "name": "Mohamed Louzari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94ac0zmknckpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26417",
  "fulltext_url": null,
  "id": "94ac0zmknckpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26417",
  "language": null,
  "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.DG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214088244",
  "pdf_url": "https://arxiv.org/pdf/2609.26417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94ac0zmknckpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Kählerian oxidation and reduction of Lie algebras with Kähler structures",
  "title_text": "Kählerian oxidation and reduction of Lie algebras with Kähler structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/94ac0zmknckpj",
  "venue": "arXiv",
  "versions": []
}