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Wikipedia mentions that there is an implication: Yang-Baxter solutions yield integrable models, what 1D systems concerns.
In arbitrary dimensions, what is the relation, if any, between solutions to Yang-Baxter equations, integrability and exact solvability?
If somebody could provide a no-go theorem or cases, where integrability was already ruled out, it would be great.
The question was primarily about the higher-dimensional case. Do you have something to add there?
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