On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps
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 ma...
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| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000221 |
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| author | Pavlos Kassotakis Theodoros E. Kouloukas Maciej Nieszporski |
| author_facet | Pavlos Kassotakis Theodoros E. Kouloukas Maciej Nieszporski |
| author_sort | Pavlos Kassotakis |
| collection | DOAJ |
| description | 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 (abelian and non-abelian) multi-parametric Yang–Baxter maps, along with their Lax representations, which lie outside the preceding lists. |
| format | Article |
| id | doaj-art-6022158b1647424bbccfdca0c0fa0128 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-6022158b1647424bbccfdca0c0fa01282025-01-29T05:02:16ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101094On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter mapsPavlos Kassotakis0Theodoros E. Kouloukas1Maciej Nieszporski2Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, PolandSchool of Computing and Digital Media, London Metropolitan University, United Kingdom; Corresponding author.Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, PolandWe 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 (abelian and non-abelian) multi-parametric Yang–Baxter maps, along with their Lax representations, which lie outside the preceding lists.http://www.sciencedirect.com/science/article/pii/S2666818125000221Yang-Baxter mapsLax matricesDiscrete integrable systems |
| spellingShingle | Pavlos Kassotakis Theodoros E. Kouloukas Maciej Nieszporski On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps Partial Differential Equations in Applied Mathematics Yang-Baxter maps Lax matrices Discrete integrable systems |
| title | On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps |
| title_full | On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps |
| title_fullStr | On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps |
| title_full_unstemmed | On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps |
| title_short | On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps |
| title_sort | on refactorization problems and rational lax matrices of quadrirational yang baxter maps |
| topic | Yang-Baxter maps Lax matrices Discrete integrable systems |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000221 |
| work_keys_str_mv | AT pavloskassotakis onrefactorizationproblemsandrationallaxmatricesofquadrirationalyangbaxtermaps AT theodorosekouloukas onrefactorizationproblemsandrationallaxmatricesofquadrirationalyangbaxtermaps AT maciejnieszporski onrefactorizationproblemsandrationallaxmatricesofquadrirationalyangbaxtermaps |