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.