Abstract
A unified approach is applied in the consideration of the multi-parametric (colored) Yang–Baxter equations (YBE) and the usual YBE with two-parametric R-matrices, relying on the existence of the arbitrary functions in the general solutions. The colored YBE are considered with the R-matrices defined on two and three-dimensional states. We present an exhaustive study and the overall solutions for the YBE with 4×4 colored R-matrices. The established classification includes new multi-parametric free fermionic solutions. In the context of the given approach there are obtained the colored solutions to the YBE with 9×9R-matrices having 15 non-zero elements.
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