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

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 $4\times 4$ 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 $9\times 9$ R-matrices having 15 non-zero elements.

30 pages, references are added, clarifications are done

References in corpus (2)

• The Yang-Baxter equation for PT invariant nineteen vertex models
• Solutions to the Yang-Baxter equations with $os{p}_q(1|2)$ symmetry: Lax operators

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