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arXiv · 2312.01337

Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures

Yunnan Li·Yunhe Sheng·Rong Tang
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Abstract

In this paper, we study relative Rota-Baxter operators of weight $0$ on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operators of weight $0$ on groups and Lie groups. We establish various explicit relations among relative Rota-Baxter operators of weight $0$ on groups, pre-groups, braces, set-theoretic solutions of the Yang-Baxter equation and $T$-structures.

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Yunnan Li, Yunhe Sheng, Rong Tang. 2023-12-03. Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures. https://doi.org/10.1007/s10231-025-01570-3

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