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arXiv · 2508.17987

Retracts of degenerate solutions of the Yang-Baxter equation

Přemysl Jedlička·Agata Pilitowska
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Abstract

Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been established so far. We fill here this gap providing a definition of multipermutation solutions that generalizes the one for non-degenerate solutions and we find an axiomatic description of this class by a set of equations that generalizes the equations describing non-degenerate multipermutation solutions. It turned out that the results do not need all the properties of solutions of the Yang-Baxter equation and therefore we prove them in a general universal-algebraic setting.

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Přemysl Jedlička, Agata Pilitowska. 2025-08-25. Retracts of degenerate solutions of the Yang-Baxter equation. https://arxiv.org/abs/2508.17987

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