On the solutions to the multi-parametric Yang-Baxter equations

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 x 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 x 9 R-matrices having 15 non-zero elements. (C) 2014 The Author. Published by Elsevier B.V.