A Lie algebra is a vector space with a skew-symmetric bilinear operation satisfying a certain identity. Lie algebras occur very frequently in Mathematics and indeed in other areas of Science and Engineering. An important class of Lie algebras are the so-called simple Lie algebras. Their classification is reasonably elementary, only using notions from Linear Algebra and some Group Theory.
The aim of this project is to arrive at the classification of complex simple Lie algebras in terms of root systems and the associated Dynkin diagrams. These concepts are important in their own right and appear in many other branches of Mathematics, not to mention Physics.
This project could be extended to a Combined Degree Mathematics and Physics, by adding some representation theory and one of the many physical applications.
Individual project for Single Degree students in Mathematics, but can be extended for Combinbed Degree students in Mathematics and Physics.
This project should only be attempted by students who have mastered Linear Algebra.