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

• Autores: Xabier García Martínez
• Directores de la Tesis: Tim Van der Linden (dir. tes.), Manuel Ladra González (dir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2017
• Idioma: inglés
• Tribunal Calificador de la Tesis: José Manuel Casas Mirás (presid.), Diana Rodelo (secret.), Andrea Montoli (voc.)
• Materias:
  • Matemáticas
    • Álgebra
      • Teoría de categorías
      • Álgebra homológica
      • Álgebra de Lie
      • Álgebras no asociativas
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • 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.