Relative Rota-Baxter operators, modules and projections

Fuente: arXiv
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Main Authors: Vilaboa, José Manuel Fernández, Rodríguez, Ramón González, Pérez, Brais Ramos
Format: Preprint
Published: 2024
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author Vilaboa, José Manuel Fernández
Rodríguez, Ramón González
Pérez, Brais Ramos
author_facet Vilaboa, José Manuel Fernández
Rodríguez, Ramón González
Pérez, Brais Ramos
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_12782
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Relative Rota-Baxter operators, modules and projections
Vilaboa, José Manuel Fernández
Rodríguez, Ramón González
Pérez, Brais Ramos
Rings and Algebras
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.
title Relative Rota-Baxter operators, modules and projections
topic Rings and Algebras
url https://arxiv.org/abs/2406.12782