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Notions of equivalence among constant Yang--Baxter Operators: To ∞-Equivalence and Beyond

  • Paul P. Martin
  • Eric C. Rowell
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Abstract

Recent advances in the classification of certain classes of Yang-Baxter operators through a holistic categorical approach has some of us wondering about ways to identify solutions. In particular the classification of charge conserving solutions in all dimensions inspires the question: \emph{what fraction of solutions are \textbf{close to} charge conserving solutions, under any \textbf{reasonable} notion of equivalence?} Of course \emph{reasonable} and \emph{close to} are open to interpretation. Here we suggest some precise notions of both, and prove that in dimension $2$, 10 out of 11 local families of solutions are close to charge conserving, and the one that misses is a singleton.

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Cite

BibTeXRIS
BibTeX
@misc{martin2026notions,
  title = {{Notions of equivalence among constant Yang--Baxter Operators: To $\infty$-Equivalence and Beyond}},
  author = {Paul P. Martin and Eric C. Rowell},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38290},
  eprint = {2609.38290},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38290},
}
RIS
TY  - UNPB
TI  - Notions of equivalence among constant Yang--Baxter Operators: To ∞-Equivalence and Beyond
AU  - Paul P. Martin
AU  - Eric C. Rowell
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38290
UR  - https://arxiv.org/abs/2609.38290
AB  - Recent advances in the classification of certain classes of Yang-Baxter operators through a holistic categorical approach has some of us wondering about ways to identify solutions. In particular the classification of charge conserving solutions in all dimensions inspires the question: \emph{what fraction of solutions are \textbf{close to} charge conserving solutions, under any \textbf{reasonable} notion of equivalence?} Of course \emph{reasonable} and \emph{close to} are open to interpretation. Here we suggest some precise notions of both, and prove that in dimension $2$, 10 out of 11 local families of solutions are close to charge conserving, and the one that misses is a singleton.
ER  -