Gaussian solutions to the Yang--Baxter equation and their twists

Yasmeen S. Baki; Padmini Veerapen

Gaussian solutions to the Yang--Baxter equation and their twists

Quantum Algebra 2026-07-15 v1 Rings and Algebras

Authors: Yasmeen S. Baki , Padmini Veerapen

Abstract

In this paper, we consider two explicit Gaussian solutions to the constant (or parameter-independent) quantum Yang--Baxter equation and produce the corresponding bialgebras using the Faddeev--Reshetikhin--Takhtajan construction (FRT). Additionally, we twist these two Gaussian solutions, via Zhang twists and corresponding 2-cocycle twists, to obtain solutions to the Yang--Baxter equation which are not necessarily Gaussian.

Keywords

Yang-Baxter equation Gaussian solutions bialgebras FRT construction Zhang twists 2-cocycle twists

Cite

@article{arxiv.2607.13876,
  title  = {Gaussian solutions to the Yang--Baxter equation and their twists},
  author = {Yasmeen S. Baki and Padmini Veerapen},
  journal= {arXiv preprint arXiv:2607.13876},
  year   = {2026}
}