Some studies on dynkin diagrams associated with Kac-moody algebra

Abstract

In the present project report, a sincere report has been made to construct and study the basic information related to Simple Lie Algebras, Kac-Moody algebras and their corresponding Dynkin Diagrams.
In chapter-1, I have given the definitions of Lie Algebra and some of the terms related to Lie algebra, i.e. subalgebras, ideals, Abelian, solvability, nilpotency etc. Also, I have done the classifications of Classical Lie algebras.
In chapter-2, I addressed the basics of Representation Theory, i.e. structure constants, modules, reflections in a Euclidean space, root systems (simple roots) and their corresponding root diagrams. Then I have discussed the formation of Dynkin Diagrams and cartan matrices associated with the roots of the simple lie algebras.
In chapter-3, I have given the necessary theory based on Kac-Moody lie algebras and their classifications. Then the definition of the extended Dynkin diagrams for Affinization of Kac-Moody algebras and the Dynkin Diagrams associated with the affine Kac-Moody algebras are provided