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PreprintCC BY 4.0arXiv

Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum

  • Jörg Feldvoss
  • Chao Ma
  • Friedrich Wagemann
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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}.

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Cite

BibTeXRIS
BibTeX
@misc{feldvoss2026tensor,
  title = {{Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum}},
  author = {Jörg Feldvoss and Chao Ma and Friedrich Wagemann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39342},
  eprint = {2610.39342},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39342},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum
AU  - Jörg Feldvoss
AU  - Chao Ma
AU  - Friedrich Wagemann
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39342
UR  - https://arxiv.org/abs/2610.39342
AB  - 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}.
ER  -