{
  "abstract": "We develop the general theory of Lie algebras in symmetric tensor categories. We prove categorical versions of classical results such as Engel's theorem, Cartan's criterion, and that all derivations of a strongly semisimple Lie algebra are inner. For finite-dimensional graded Lie algebras, we construct a graded category $\\mathcal{O}$, classify its graded-simple objects, and prove the generic graded irreducibility of Verma modules. Lastly, we develop the theory of root systems for contragredient Lie algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27492",
  "author_total": 6,
  "authors": [
    {
      "name": "Iván Angiono"
    },
    {
      "name": "Agustina Czenky"
    },
    {
      "name": "Pavel Etingof"
    },
    {
      "name": "Victor Ostrik"
    },
    {
      "name": "Julia Plavnik"
    },
    {
      "name": "Guillermo Sanmarco"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cyk6d20yf3xa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27492",
  "fulltext_url": null,
  "id": "8cyk6d20yf3xa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27492",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223148300",
  "pdf_url": "https://arxiv.org/pdf/2610.27492",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cyk6d20yf3xa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27492",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27492"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lie algebras in symmetric tensor categories",
  "title_text": "Lie algebras in symmetric tensor categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/8cyk6d20yf3xa",
  "venue": "arXiv",
  "versions": []
}