{
  "abstract": "We introduce Kleisli convolution representations for groups, rings, and algebras. We show that their representation categories are equivalent to the usual ones for groups and finite-dimensional algebras, but for rings only recover modules whose underlying Abelian groups are free of finite rank. We also apply the Kleisli convolution representation to provide a partial answer to the Margolis--Sakurai version of the modular isomorphism problem: If $G$ is a finite $p$-group with $D_3(G)=1$ and $\\gcd(m,c_G!)=1$, then $\\mathbb F_{p^m}G\\cong\\mathbb F_{p^m}H$ implies $G\\cong H$, where $c_G$ is the number of geometric connected components of $\\mathrm{Aut}(\\overline{\\mathbb F}_pG)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09525",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu-Zhe Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56v0dkfyj49cq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09525",
  "fulltext_url": null,
  "id": "56v0dkfyj49cq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09525",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7212138444",
  "pdf_url": "https://arxiv.org/pdf/2609.09525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56v0dkfyj49cq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.09525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Kleisli convolution representations and a Margolis--Sakurai version of the modular isomorphism problem",
  "title_text": "Kleisli convolution representations and a Margolis--Sakurai version of the modular isomorphism problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/56v0dkfyj49cq",
  "venue": "arXiv",
  "versions": []
}