{
  "abstract": "We investigate structural properties of Lie affgebras, viewed as affine analogues of Lie algebras. We introduce the notion of an ideaf, the affine counterpart of an ideal, and establish characterizations of left and right ideafs. We further study centers, quotient structures, and product ideafs, proving, under suitable conditions, that the center of a Lie affgebra is an ideaf. We then develop the notion of affine nilpotency and establish connections between the nilpotency of Lie affgebras and that of their retracted Lie algebras. As an application, we prove an Engel-type theorem for Lie affgebras of the form $\\mathfrak{a}(\\mathfrak{g};κ=2λ,λ,s)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15190",
  "author_total": 3,
  "authors": [
    {
      "name": "Tarik Anowar"
    },
    {
      "name": "Ripan Saha"
    },
    {
      "name": "Sayan Thokdar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ek7ve0d19jzdq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15190",
  "fulltext_url": null,
  "id": "ek7ve0d19jzdq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15190",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7203672765",
  "pdf_url": "https://arxiv.org/pdf/2608.15190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ek7ve0d19jzdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.15190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15190"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nilpotency and Engel-Type Theorems for Lie Affgebras",
  "title_text": "Nilpotency and Engel-Type Theorems for Lie Affgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ek7ve0d19jzdq",
  "venue": "arXiv",
  "versions": []
}