Braided Crossed Modules and Loday-Pirashvili category

  1. Alejandro Fernández Fariña
Supervised by:
  1. Manuel Ladra González Director

Defence university: Universidade de Santiago de Compostela

Year of defence: 2021

  1. José Manuel Casas Mirás Chair
  2. María Pilar Carrasco Carrasco Secretary
  3. Emzar Khmaladze Committee member
  1. Department of Mathematics

Type: Thesis


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.