{
  "abstract": "We continue our investigation of certain associativity properties (namely, alternativity, power-associativity, or being a Jordan ring) of the non-associative multiplication defined on the Grothendieck group of the category of finite-dimensional Leibniz bimodules which we started in \\cite{FW}. Namely, we prove that for every finite-dimensional non-zero Leibniz algebra over an arbitrary field this Grothendieck ring is not power-associative. As a consequence, the Grothendieck ring is also neither alternative nor a Jordan ring. This corrects and generalizes some of our results in the last section of \\cite{FW}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39342",
  "author_total": 3,
  "authors": [
    {
      "name": "Jörg Feldvoss"
    },
    {
      "name": "Chao Ma"
    },
    {
      "name": "Friedrich Wagemann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfmse643ppyk9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39342",
  "fulltext_url": null,
  "id": "dfmse643ppyk9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39342",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39342",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfmse643ppyk9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39342",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39342"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum",
  "title_text": "Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dfmse643ppyk9",
  "venue": "arXiv",
  "versions": []
}