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NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators

  • Bei Li
  • Dingguo Wang
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Abstract

We introduce NS-Leibniz bialgebras and establish their equivalence with matched pairs and Manin triples of NS-Leibniz algebras. In the coboundary case, skew-symmetric solutions of the NS-Leibniz Yang--Baxter equation yield NS-Leibniz bialgebras and correspond to π’ͺ-operators for the dual regular representation. We study quasi-triangular and factorizable structures, and relate factorizable tensors to quadratic Rota--Baxter NS-Leibniz algebras of any fixed nonzero weight. We also construct compatible bialgebra structures from skew-adjoint Nijenhuis operators commuting with the Rota--Baxter operator.

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Cite

BibTeXRIS
BibTeX
@misc{li2026nsleibniz,
  title = {{NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators}},
  author = {Bei Li and Dingguo Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39190},
  eprint = {2610.39190},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39190},
}
RIS
TY  - UNPB
TI  - NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators
AU  - Bei Li
AU  - Dingguo Wang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39190
UR  - https://arxiv.org/abs/2610.39190
AB  - We introduce NS-Leibniz bialgebras and establish their equivalence with matched pairs and Manin triples of NS-Leibniz algebras. In the coboundary case, skew-symmetric solutions of the NS-Leibniz Yang--Baxter equation yield NS-Leibniz bialgebras and correspond to π’ͺ-operators for the dual regular representation. We study quasi-triangular and factorizable structures, and relate factorizable tensors to quadratic Rota--Baxter NS-Leibniz algebras of any fixed nonzero weight. We also construct compatible bialgebra structures from skew-adjoint Nijenhuis operators commuting with the Rota--Baxter operator.
ER  -