Quantum Groups

What it is about

You learn the theory of quantum groups: Hopf algebras, q-deformations and quantized enveloping algebras. In the end you will be able to explain central constructions and examples, describe their representation theory and connections to classical Lie algebras as well as applications such as knot invariants.

What you will be able to do

• Repeat basic concepts and definitions of quantum groups with confidence
• Understand and apply Hopf algebra structures and q-deformations
• Apply representation theory of quantized algebras and classification of simple representations
• Construct and analyze central examples of quantum groups and their representations
• Construct and use Lusztig's PBW bases
• Understand the relationship between quantum groups and classical Lie algebras
• Develop proof techniques and apply theoretical concepts to new problems

What the module consists of

• VorlesungConveying the theoretical foundations and proof techniques
• ÜbungPractice of methods on problems, deepening the course material

Teaching method

• TafelvorlesungSystematic introduction of concepts and derivations
• Regular exercise sessions with problem sheetsSolidifying the material and developing problem-solving skills