Categorical-algebraic methods in non-commutative and non-associative algebra

  1. Xabier García Martínez
Dirixida por:
  1. Tim Van der Linden Director
  2. Manuel Ladra González Director

Universidade de defensa: Universidade de Santiago de Compostela

Ano de defensa: 2017

  1. José Manuel Casas Mirás Presidente/a
  2. Diana Rodelo Secretario/a
  3. Andrea Montoli Vogal
  1. Departamento de Matemáticas

Tipo: Tese


The objective of this dissertation is twofold: firstly to use categorical and algebraic methods to study homological properties of some of the aforementioned semi-abelian, non-associative structures and secondly to use categorical and algebraic methods to study categorical properties and provide categorical characterisations of some well-known algebraic structures. On one hand, the theory of universal central extensions together with the non-abelian tensor product will be studied and used to explicitly calculate some homology groups and some problems about universal enveloping algebras and actions will be solved. On the other hand, we will focus on giving categorical characterisations of some algebraic structures, such as a characterisation of groups amongst monoids, of cocommutative Hopf algebras amongst cocommutative bialgebras \cite{GaVa-bialgebras} and of Lie algebras amongst alternating algebras.