English

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

Mathematical Physics 2015-06-17 v2 math.MP

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 4×44 \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 9×99 \times 9 R-matrices having 15 non-zero elements.

Keywords

Cite

@article{arxiv.1311.4994,
  title  = {On the solutions to the multi-parametric Yang-Baxter equations},
  author = {Sh. Khachatryan},
  journal= {arXiv preprint arXiv:1311.4994},
  year   = {2015}
}

Comments

30 pages, references are added, clarifications are done

R2 v1 2026-06-22T02:11:04.305Z