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dc.contributor.advisorLadra González, Manuel
dc.contributor.authorFernández Fariña, Alejandro
dc.description.abstractThis thesis is devoted to the study of braidings in different mathematical contexts, as well as in a deeper analysis of the Loday-Pirashvili category. We will study the notion of braidings for crossed modules and internal categories in the cases of groups, associative algebras, Lie algebras and Leibniz algebras, showing the equivalence between the respective categories. We will also study universal central extensions in the category of braided crossed modules of Lie algebras. Finally, we will show how to generalize the Loday-Pirashvili category. With that construction, we will exhibit a generalization of the relationship between Lie and Leibniz objects.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.subjectBraided category
dc.subjectCrossed Module
dc.subjectLie Algebra
dc.subjectLeibniz Algebra
dc.subjectuniversal central extension
dc.subjectLoday-Pirashvili category
dc.subject.classificationMaterias::Investigación::12 Matemáticas::1201 Algebra::120103 Teoría de categorías
dc.subject.classificationMaterias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie
dc.subject.classificationMaterias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativas
dc.titleBraided Crossed Modules and Loday-Pirashvili category
dc.contributor.affiliationUniversidade de Santiago de Compostela. Escola de Doutoramento Internacional (EDIUS)
dc.contributor.affiliationUniversidade de Santiago de Compostela. Programa de Doutoramento en Matemáticas

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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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