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<p>The present article is devoted to introduce, in a braided monoidal setting, the notion of module over a relative Rota-Baxter operator. It is proved that there exists an adjunction between the category of modules associated to an invertible relative Rota-Baxter operator and the category of modules associated to a Hopf brace, which induces an equivalence by assuming certain additional hypothesis. Moreover, the notion of projection between relative Rota-Baxter operators is defined, and it is proved that those which are called “strong” give rise to a module according to the previous definition in the cocommutative setting.</p>

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Relative Rota-Baxter operators, modules and projections

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月14日

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  • José Manuel Fernández Vilaboa,
  • Ramón González Rodríguez,
  • Brais Ramos Pérez

摘要

The present article is devoted to introduce, in a braided monoidal setting, the notion of module over a relative Rota-Baxter operator. It is proved that there exists an adjunction between the category of modules associated to an invertible relative Rota-Baxter operator and the category of modules associated to a Hopf brace, which induces an equivalence by assuming certain additional hypothesis. Moreover, the notion of projection between relative Rota-Baxter operators is defined, and it is proved that those which are called “strong” give rise to a module according to the previous definition in the cocommutative setting.