Groups and Algebras for Theoretical Physics

This course builds on the basic concepts of Lie groups and Lie algebras as treated in the course Advanced Concepts of Theoretical Physics and goes on to treat subjects such as the Cartan subalgebra, root diagrams, Dynkin diagrams and the classification of complex semi-simple Lie algebras. Next, affine Lie algebras are studied in detail. Advanced topics include the Virasoro algebra, Lie super-algebras and quantum groups.

• The classification of complex semi-simple Lie algebras
• Affine Lie algebras
• the Virasoro algebra
• Lie super-algebras
• Quantum groups

• Di Francesco et al: Conformal Field Theories (Springer)
• Fuchs, Schweigert: Symmetries, Lie Algebras and Representations (Cambridge University Press)
• Fuchs : Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory (Cambridge University Press)

• Lecture Notes

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9
• Exercise 10
• Exercise 11