PreprintCC BY 4.0arXiv
Gaussian solutions to the Yang--Baxter equation and their twists
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.
Related
- Dual Reflection Groups from Solutions to the Yang--Baxter Equation
- NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators
- Solving the 4 × 4 quantum Yang-Baxter equation
- A categorical approach to the set-theoretic Yang-Baxter equation
- Every group is the automorphism group of a set-theoretic solution of the Yang--Baxter equation
BibTeX
@misc{baki2026gaussian,
title = {{Gaussian solutions to the Yang--Baxter equation and their twists}},
author = {Yasmeen S. Baki and Padmini Veerapen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.13876},
eprint = {2607.13876},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.13876},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gaussian solutions to the Yang--Baxter equation and their twists
AU - Yasmeen S. Baki
AU - Padmini Veerapen
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2607.13876
UR - https://arxiv.org/abs/2607.13876
AB - 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.
ER -