{
  "abstract": "Let $K$ be a field and let $\\T=L_K(E_T)$ be the algebraic Toeplitz algebra. We classify the Lie ideals of $\\T^-$. If $w$ is the sink of the Toeplitz graph and $F=I(w)$, then $F\\cong M_\\infty(K)$, $\\T/F\\cong K[t,t^{-1}]$, and $[\\T,\\T]=F$. We prove that every noncentral Lie ideal contains $\\mathfrak s=[F,F]$, the finitary trace-zero Lie algebra. Thus the classification reduces to the Heisenberg-type quotient $\\T/\\mathfrak s$. The Lie ideals are precisely $0$, $K1$, the spaces $\\mathfrak s+U$, where $U\\leq P_K\\oplus Kw$ and $w\\notin U$, and the inverse images $ρ^{-1}(W)$, where $W\\leq K[t,t^{-1}]$. Here $P_K=K1$ in characteristic $0$, and $P_K=\\operatorname{span}_K\\{1,e^{m\\ell},(e^*)^{m\\ell}:m\\geq1\\}$ if $\\operatorname{char}K=\\ell>0$. We also describe the Lie derivations of $\\T^-$ as sums of associative derivations of $\\T$ and central Lie derivations factoring through $\\T/F$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04745",
  "author_total": 2,
  "authors": [
    {
      "name": "Thao Nhi Nguyen Huynh"
    },
    {
      "name": "Viet Khanh Huynh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5p4rt7pgsjw8q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04745",
  "fulltext_url": null,
  "id": "5p4rt7pgsjw8q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04745",
  "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": "W7211902761",
  "pdf_url": "https://arxiv.org/pdf/2609.04745",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5p4rt7pgsjw8q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04745",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04745"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lie Ideals and Lie Derivations of the Algebraic Toeplitz Algebra",
  "title_text": "Lie Ideals and Lie Derivations of the Algebraic Toeplitz Algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/5p4rt7pgsjw8q",
  "venue": "arXiv",
  "versions": []
}