Gradings on simple real Lie algebras

TL;DR

This doctoral thesis provides a simplified classification of gradings on simple real Lie algebras, consolidating four articles' results into an accessible overview for mathematicians.

Contribution

It offers a comprehensive classification of gradings on simple real Lie algebras, presenting the results in an accessible language and format.

Findings

Complete classification of gradings achieved

Simplified explanations of complex algebraic structures

Results applicable to broader Lie algebra research

Abstract

English: This work is a doctoral thesis in mathematics by compendium of four articles. Here we explain, using a language as simple as possible, the results achieved in those articles. The general objective is the classification of gradings on simple real Lie algebras. The text is written in both english and spanish. ----- Espa\~nol: Esta obra es una tesis doctoral en matem\'aticas por compendio de cuatro art\'iculos. Aqu\'i explicamos, utilizando un lenguaje lo m\'as sencillo posible, los resultados alcanzados en esos art\'iculos. El objetivo general es la clasificaci\'on de las graduaciones en las \'algebras de Lie reales simples. El texto est\'a escrito tanto en ingl\'es como en espa\~nol.