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

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).