Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions
Abstract
We find all solutions to the constant Yang--Baxter equation in three dimensions, subject to an additive charge-conservation ansatz. This ansatz is a generalisation of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. Additive charge-conservation introduces additional sector-coupling parameters -- in 3 dimensions there are such parameters. In the generic dimension 3 case, in which all of the parameters are nonzero, we find there is a single 3 parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centraliser (symmetry) algebra in all orders. We also solve the remaining cases with three, two, or one nonzero sector-coupling parameter(s).
Keywords
Cite
@article{arxiv.2310.03816,
title = {Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions},
author = {Jarmo Hietarinta and Paul Martin and Eric C. Rowell},
journal= {arXiv preprint arXiv:2310.03816},
year = {2024}
}
Comments
Corrected version for publication