Abstract
Abstract
We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang–Baxter equation (YBE). Such solutions can be always obtained using certain algebraic structures that generalize nilpotent rings called braces. Our main aim here is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary results. We first identify the generic form of the twists associated to set-theoretic solutions and we show that these twists are admissible, i.e. they satisfy a certain co-cycle condition. These findings are also valid for Baxterized solutions of the YBE constructed from the set-theoretical ones.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. The Floquet Baxterisation;SciPost Physics;2024-03-18
2. From braces to pre-Lie rings;Proceedings of the American Mathematical Society;2024-01-11
3. More on skew braces and their ideals;Contemporary Mathematics;2024
4. Near braces and p$p$‐deformed braided groups;Bulletin of the London Mathematical Society;2023-09-07
5. Set-theoretic Yang–Baxter & reflection equations and quantum group symmetries;Letters in Mathematical Physics;2021-08