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<p>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 <i>T</i>-structures.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月11日

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  • Yunnan Li,
  • Yunhe Sheng,
  • Rong Tang

摘要

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.