2025/08/25 by Jedlička, Přemysl, Pilitowska, Agata
#08A30 #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 16T25. Secondary: 06B10
paper · doi:10.48550/arxiv.2508.17987
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.