Quantum Groups
The course is an introduction to the elements of Hopf algebra theory. The
aim is to understand the modern examples of such objects associated to the
term “quantum group”. In particular, these can be quantized enveloping
algebras of Lie algebras or certain deformations of the function algebras
on matrix groups.
1. Bialgebras and Hopf algebras.
2. Classical examples from group and Lie algebra theory.
3. Representations : modules and comodules ; tensor categories.
4. Braided tensor categories ; (Co)quasitriangular Hopf algebras,
R-matrices and the Drinfeld double.
5. Examples of quantum enveloping algebras and deformed matrix groups.