{
  "abstract": "We study left-invariant Gray $\\mathcal{A}$-metrics (cyclic-parallel Ricci tensor) on nilpotent Lie groups, focusing on the algebraic condition that the Ricci operator belongs to the quasicentroid $\\operatorname{QC}(\\mathfrak{n})$ of the Lie algebra $\\mathfrak{n}$. We review and develop the abstract structure theory of quasicentroids, and prove a Central Decomposition Theorem: any nilpotent Riemannian Lie algebra with $\\operatorname{Ric} \\in \\operatorname{QC}(\\mathfrak{n})$ decomposes as a central product of ideals $\\mathfrak{i}_j = E_{λ_j} \\oplus \\mathfrak{z}$, where $\\mathfrak{z}$ is the center of $\\mathfrak{n}$ and $E_{λ_j}$ are the negative Ricci eigenspaces. Endowed with the restricted metric, each factor $\\mathfrak{i}_j$ is itself a Gray $\\mathcal{A}$-space. Finally, we investigate when the general $\\mathcal{A}$-metric condition reduces to $\\operatorname{Ric} \\in \\operatorname{QC}(\\mathfrak{n})$. We prove this equivalence unconditionally for two-step nilpotent algebras and whenever the metric admits a nice basis, and provide a general characterization via the vanishing of two trace identities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39184",
  "author_total": 1,
  "authors": [
    {
      "name": "Edison Alberto Fernández-Culma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2m6j42tbyexhd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39184",
  "fulltext_url": null,
  "id": "2m6j42tbyexhd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39184",
  "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.DG"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2m6j42tbyexhd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Gray $\\mathcal{A}$-metrics on nilpotent Lie groups and the quasicentroid condition",
  "title_text": "Gray 𝒜-metrics on nilpotent Lie groups and the quasicentroid condition",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2m6j42tbyexhd",
  "venue": "arXiv",
  "versions": []
}