On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917903222177792 |
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| author | Kassotakis, Pavlos Kouloukas, Theodoros E. Nieszporski, Maciej |
| author_facet | Kassotakis, Pavlos Kouloukas, Theodoros E. Nieszporski, Maciej |
| contents | We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang-Baxter maps ($\mathcal{K}$-list), by considering the symmetries of the $\mathcal{K}$-list maps, we obtain compatible refactorization problems with rational Lax matrices for other classes of non-abelian involutive Yang-Baxter maps ($Λ$, $\mathcal{H}$ and $\mathcal{F}$ lists). In the abelian setting, this procedure generates rational Lax representations for the abelian Yang-Baxter maps of the $F$ and $H$ lists. Additionally, we provide examples of non-involutive (abelian and non-abelian) multi-parametric Yang-Baxter maps, along with their Lax representations, which lie outside the preceding lists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15344 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps Kassotakis, Pavlos Kouloukas, Theodoros E. Nieszporski, Maciej Exactly Solvable and Integrable Systems Mathematical Physics We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang-Baxter maps ($\mathcal{K}$-list), by considering the symmetries of the $\mathcal{K}$-list maps, we obtain compatible refactorization problems with rational Lax matrices for other classes of non-abelian involutive Yang-Baxter maps ($Λ$, $\mathcal{H}$ and $\mathcal{F}$ lists). In the abelian setting, this procedure generates rational Lax representations for the abelian Yang-Baxter maps of the $F$ and $H$ lists. Additionally, we provide examples of non-involutive (abelian and non-abelian) multi-parametric Yang-Baxter maps, along with their Lax representations, which lie outside the preceding lists. |
| title | On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2501.15344 |