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Adamopoulou, Panagiota, Kouloukas, Theodoros and Papamikos, Georgios (2025) Reductions and degenerate limits of Yang–Baxter maps with 3 × 3 Lax matrices. Journal of Physics A: Mathematical and Theoretical, 58(20) (205202). pp. 1-14. ISSN 1751-8113
Abstract
We generalise a family of quadrirational parametric Yang–Baxter (YB) maps with 3 × 3 Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational YB maps, and we discuss some of their integrability properties. This work is part of a more general classification of YB maps admitting a strong 3 × 3 Lax matrix with a linear dependence on the spectral parameter.
Available under License Creative Commons Attribution 4.0.
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