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Averaging Zinbiel bialgebras

  • Bei Li
  • Dingguo Wang
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Abstract

In this paper, we introduce and study averaging Zinbiel bialgebras. We first define representations of averaging Zinbiel algebras and prove a semi-direct product characterization. We then introduce matched pairs and Manin triples of averaging Zinbiel algebras, and characterize averaging Zinbiel bialgebras by these two structures. We show that every averaging Zinbiel algebra induces a pre-Lie algebra, and that every averaging Zinbiel bialgebra induces a pre-Lie bialgebra. We also study coboundary averaging Zinbiel bialgebras and introduce the S admissible Zinbiel Yang-Baxter equation. Its symmetric solutions give rise to averaging Zinbiel bialgebras. Finally, we investigate averaging operators on quadratic Rota-Baxter Zinbiel algebras and relative Rota-Baxter operators on averaging Zinbiel algebras.

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Cite

BibTeXRIS
BibTeX
@misc{li2026averaging,
  title = {{Averaging Zinbiel bialgebras}},
  author = {Bei Li and Dingguo Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39220},
  eprint = {2610.39220},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39220},
}
RIS
TY  - UNPB
TI  - Averaging Zinbiel bialgebras
AU  - Bei Li
AU  - Dingguo Wang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39220
UR  - https://arxiv.org/abs/2610.39220
AB  - In this paper, we introduce and study averaging Zinbiel bialgebras. We first define representations of averaging Zinbiel algebras and prove a semi-direct product characterization. We then introduce matched pairs and Manin triples of averaging Zinbiel algebras, and characterize averaging Zinbiel bialgebras by these two structures. We show that every averaging Zinbiel algebra induces a pre-Lie algebra, and that every averaging Zinbiel bialgebra induces a pre-Lie bialgebra. We also study coboundary averaging Zinbiel bialgebras and introduce the S admissible Zinbiel Yang-Baxter equation. Its symmetric solutions give rise to averaging Zinbiel bialgebras. Finally, we investigate averaging operators on quadratic Rota-Baxter Zinbiel algebras and relative Rota-Baxter operators on averaging Zinbiel algebras.
ER  -