Hopf algebras and representations
Representation theory is the systematic study of linear actions of symmetries. The classical study of symmetries begins with the representations of finite groups (discrete symmetries) and Lie algebras (continuous symmetries). These have applications in topology, number theory, quantum physics, and chemistry, among others.
Hopf algebras are an algebraic framework that captures the essential abstract features underlying representation theoretic operations. In particular they unify much of the study of representations of finite groups and Lie algebras, but there are Hopf algebras more general than either of these classical examples. Certain particularly interesting Hopf algebras, affectionately called "quantum groups", have applications in knot theory, integrable systems, and conformal field theory, as well as the representation theory of finite groups itself.
This course is an introduction to representation theory and Hopf algebras. We begin by the fundamentals of representation theory of finite groups. We then introduce Hopf algebras, and study some of their basic properties. Finally, we introduce the notion of braided Hopf algebras and construct one of the simplest quantum groups, and discuss how knot invariants can be constructed with its representations.
Tuesdays 14-16 in M3- Tuesdays 12-14 in Y307
- Note: The time of Tuesdays lectures has been changed. The new lecture hall Y307 is somewhat nontrivial to find, one must take the correct staircase to the third floor. Follow the signs on the corridors of the maths department!
- Thursdays 14-16 in M3
- Fridays 12-14 in M3
The course is 5 credits. The final grade is determined either by
- exercises (weight 50%) and final exam (weight 50%) or
- final exam only,