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arXiv · 2406.12782

Relative Rota-Baxter operators, modules and projections

José Manuel Fernández Vilaboa·Ramón González Rodríguez·Brais Ramos Pérez
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Abstract

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.

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José Manuel Fernández Vilaboa, Ramón González Rodríguez, Brais Ramos Pérez. 2024-06-18. Relative Rota-Baxter operators, modules and projections. https://doi.org/10.21136/cmj.2025.0467-24

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