Retracts of degenerate solutions of the Yang-Baxter equation
Mathematical Physics
2025-08-26 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2508.17987,
title = {Retracts of degenerate solutions of the Yang-Baxter equation},
author = {Přemysl Jedlička and Agata Pilitowska},
journal= {arXiv preprint arXiv:2508.17987},
year = {2025}
}