Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions



: Hietarinta, J.; Martin, P.; Rowell, E. C.

Publisher: ROYAL SOC

: LONDON

: 2024

: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

: P ROY SOC A-MATH PHY

:  20230810

: 480

: 2294

: 24

: 1364-5021

: 1471-2946

DOI: https://doi.org/10.1098/rspa.2023.0810

: https://doi.org/10.1098/rspa.2023.0810

: https://research.utu.fi/converis/portal/detail/Publication/457760357

: https://arxiv.org/abs/2310.03816


We find all solutions to the constant Yang-Baxter equation R12R13R23=R23R13R12 in three dimensions, subject to an additive charge-conservation (ACC) ansatz. This ansatz is a generalization of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. ACC introduces additional sector-coupling parameters-in three dimensions, there are four such parameters. In the generic dimension 3 case, in which all of the four parameters are non-zero, we find there is a single three parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centralizer (symmetry) algebra in all orders. We also solve the remaining cases with three, two or one non-zero sector-coupling parameter(s).

Last updated on 2025-27-01 at 19:22