| Description |
Lie Groups provide a structure to study differential equations, and so have a variety of important applications in modern mathematics and theoretical physics. Classifying the set of Lie Groups is therefore an inherently interesting and useful question. This paper seeks to classify these groups by classifying the Lie Algebras over the complex numbers; algebras which can be associated with a given Lie Group. Each simple Lie Algebra comes equipped with a root space and associated Dynkin Diagram; these diagrams similarly have properties that can be used to construct the set of Lie Algebras. We will show that this set consists of the root spaces associated with the classical Lie Algebras and the 5 exceptional Lie Algebras. Given this construction, we then present a program which allows the conversion of the adjoint representation of a Lie Algebra in C2 to a dynkin diagram. This program will also provide support for determining the adjoint representation equivalent to a given Dynkin Diagram. |
