{
  "abstract": "There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group $H_{2n+1}$, or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra $\\mathfrak{h}_{2n+1}$, denoted by $μ$, $ν$, and $ϕ$. We show that, in a specific case, $μ$ is an algebraic Ricci soliton that is shrinking. Moreover, $ν$ is an algebraic Ricci soliton only on the three-dimensional Heisenberg Lie algebra $\\mathfrak{h}_3$ and it is shrinking. Finally, we show that $ϕ$ is a steady algebraic Ricci soliton on $\\mathfrak{h}_{2n + 1}$ for $n > 1$. However, for $n = 1$, $ϕ$ is flat.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17183",
  "author_total": 1,
  "authors": [
    {
      "name": "Youssef Ayad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxw2dcrd0sjf7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17183",
  "fulltext_url": null,
  "id": "cxw2dcrd0sjf7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17183",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7213415262",
  "pdf_url": "https://arxiv.org/pdf/2609.17183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxw2dcrd0sjf7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17183"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lorentzian Algebraic Ricci Solitons on the Heisenberg Group",
  "title_text": "Lorentzian Algebraic Ricci Solitons on the Heisenberg Group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/cxw2dcrd0sjf7",
  "venue": "arXiv",
  "versions": []
}