A1 Refereed original research article in a scientific journal
Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions
Authors: Hietarinta, J.; Martin, P.; Rowell, E. C.
Publisher: ROYAL SOC
Publishing place: LONDON
Publication year: 2024
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Journal name in source: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Journal acronym: P ROY SOC A-MATH PHY
Article number: 20230810
Volume: 480
Issue: 2294
Number of pages: 24
ISSN: 1364-5021
eISSN: 1471-2946
DOI: https://doi.org/10.1098/rspa.2023.0810
Web address : https://doi.org/10.1098/rspa.2023.0810
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457760357
Preprint address: 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).
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