Semisimple Lie Group theory with application in geometric invariant theory

Abstract

The goal of this thesis was to learn about the theory of Lie algebras, Lie groups and some real geometric invariant theory, with emphasis on semisimple Lie group theory. The material in this thesis was not known to me beforehand, so the thesis represents the material which I have learned from scratch. The main motivation for studying the material in this thesis was to get insight into a problem in pseudo- Riemannian geometry intersecting real geometric invariant theory. This problem consists of classifying tensors under the action of a semisimple Lie group. [....]