Real forms of simple lie algebras

Abstract

This thesis is about the real forms of simple Lie algebras. Firstly we start with some basic theory of Lie algebra and different types of Lie algebras with some examples in Chapter 2. Thereafter in Chapters 3 to 4 we give the complete classification of real forms of simple Lie algebras. Also we have discuss the Chevalley basis which is important for the Simple Lie algebras. This project introduces Lie groups and their associated Lie algebras. In this thesis we introduce various properties of real forms, conjugations, and automorphisms of complex simple Lie algebras. Finally, there is a complete classification of real forms of simple Lie algebras.