{
  "abstract": "It is an open question whether the Lie algebra $\\mathrm{HH}^1(B)$ of a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ is simple only if the block is nilpotent with an elementary abelian defect group of order at least $3$. We show this to be the case if $B$ has a normal abelian defect group. Another open question is whether $\\mathrm{HH}^1(kS_n)$ is a solvable Lie algebra, where $S_n$ denotes a symmetric group on $n$ letters. We give some general solvability criteria for $\\mathrm{HH}^1(B)$ of blocks $B$ with a normal defect group, and, making use of results of Chuang-Kessar and Chuang-Rouquier, we deduce that if $B$ is a block of a symmetric group algebra with an abelian defect group, then $\\mathrm{HH}^1(B)$ is solvable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32673",
  "author_total": 2,
  "authors": [
    {
      "name": "Markus Linckelmann"
    },
    {
      "name": "Jialin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j2t2awk88cn2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32673",
  "fulltext_url": null,
  "id": "4j2t2awk88cn2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32673",
  "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.RT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223690430",
  "pdf_url": "https://arxiv.org/pdf/2610.32673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j2t2awk88cn2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32673"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Lie algebra structure of $\\mathrm{HH}^1(B)$ for blocks with a normal defect group",
  "title_text": "The Lie algebra structure of HH^1(B) for blocks with a normal defect group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/4j2t2awk88cn2",
  "venue": "arXiv",
  "versions": []
}