What it is about
You will receive an introduction to the fundamentals and examples of Lie algebras of small and medium size and their representations. By the end you will know the classification by root systems and Dynkin diagrams, understand highest weights for representations, and the complete classification of real and complex Clifford algebras.
What you will be able to do
- Know basic concepts of Lie algebras
- Be able to distinguish real and complex Lie algebras
- Understand root-space decomposition of semisimple Lie algebras
- Know the classification of root systems and Dynkin diagrams
- Describe representations of semisimple Lie algebras by highest weights
- Understand the complete classification of real and complex Clifford algebras
What the module consists of
- VorlesungPresentation of axioms, examples, theory and classification; step-by-step construction from fundamentals to representations
- Skript/Folien/TafelanschriebSupporting learning materials for the lecture
Teaching method
- VorlesungIntroduction from the axioms to concrete low-dimensional examples and gradual development of the classification and representation theory