2024/06/18 by J. M. Fernández Vilaboa, Vilaboa, José Manuel Fernández, R. González Rodrı́guez +3
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.12782
openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.