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arXiv · 2509.21708

Braided dynamical groups, the dynamical Yang-Baxter equation and related structures

Chengming Bai·Li Guo·Yunhe Sheng·You Wang
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Abstract

We introduce the notion of a braided dynamical group which is a matched pair of dynamical groups satisfying extra conditions. It is shown to give a solution of the dynamical Yang-Baxter equation and at the same time a braided groupoid, thereby integrating the approaches of Andruskiewitsch and Matsumoto-Shimizu respectively that use these two notions to produce quiver-theoretical solutions of the Yang-Baxter equation. We pursue this connection further by relative Rota-Baxter operators on dynamical groups, which give rise to matched pairs of dynamical groups. As the derived structures of relative Rota-Baxter operators on dynamical groups, dynamical post-groups are introduced and are shown to be equivalent to braided dynamical groups. Finally, skew-braces are generalized to dynamical skew-braces as another equivalent notion of braided dynamical groups.

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Chengming Bai, Li Guo, Yunhe Sheng, You Wang. 2025-09-26. Braided dynamical groups, the dynamical Yang-Baxter equation and related structures. https://arxiv.org/abs/2509.21708

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