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Kassotakis, Pavlos, Kouloukas, Theodoros E. and Nieszporski, Maciej (2025) On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps. Partial Differential Equations in Applied Mathematics, 13 (101094). pp. 1-6. ISSN 2666-8181
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 (K-list), by considering the symmetries of the K-list maps, we obtain compatible refactorization problems with rational Lax matrices for other classes of non-abelian involutive Yang–Baxter maps (Λ, H and 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 multi-parametric Yang–Baxter maps, along with their Lax representations, which lie outside the preceding lists.
Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.
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