Hopf braces, related structures, and their associated categories
This dissertation is devoted to the study of Hopf braces and their generalizations within the framework of braided monoidal categories. We begin by conducting an exhaustive analysis of the categorical relationships between the category of Hopf braces and other categories (invertible 1-cocycles, matc...
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| Formato: | tesis doctoral |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/45436 |
| Acesso em linha: | https://hdl.handle.net/10347/45436 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hopf brace projection Yetter-Drinfeld module Hopf truss Hopf bracoid 120103 Teoría de categorías |
| Resumo: | This dissertation is devoted to the study of Hopf braces and their generalizations within the framework of braided monoidal categories. We begin by conducting an exhaustive analysis of the categorical relationships between the category of Hopf braces and other categories (invertible 1-cocycles, matched pairs, post-Hopf algebras and relative Rota-Baxter operators) - for which the existing results in the literature are extended to a braided monoidal framework - together with others that are new, such as the description of the category of Hopf braces as that of brace triples and op-brace triples. Next, we focus on the construction of new Hopf braces via crossed products, obtaining results that allows us to identify the conditions under which the Drinfeld Double Hopf algebra is part of a Hopf brace structure. Afterwards, attention is diverted to the study of the category of modules over a Hopf brace. |
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