Braided Crossed Modules and Loday-Pirashvili category

This 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 Leib...

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Detalles Bibliográficos
Autor: Fernández Fariña, Alejandro
Tipo de recurso: tesis doctoral
Fecha de publicación:2021
País:España
Institución: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:10347/26581
Acceso en línea:http://hdl.handle.net/10347/26581
Access Level:acceso abierto
Palabra clave:Materias::Investigación::12 Matemáticas::1201 Algebra::120103 Teoría de categorías
Materias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie
Materias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativas
Descripción
Sumario:This 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.