Lecture Course:

V4A4 Representation Theory II

Topics:

The lecture course is roughly divided in two parts.

Part I:

We will discuss the general theory of Hopf algebras. This will include the discussion of the monoidal category of modules for a Hopf algebra, the concept of restricted duals and will finish with a series of structure theorems classifying a large class of certain Hopf algebras.
There are no special prerequisites for this part of the lecture, except a general knowledge of basic algebra.

Part II:

In the second half of the course we will focus on one family of Hopf algebras, so-called quantum groups or quantized universal enveloping algebras. These are certain deformations of Lie algebras and we will discuss their properties as well as study their representation theory. We will finish this part with a number of application of quantum groups in the representation theory of Lie algebras, knot invariants and other topics, depending on the available time.
Although not strictly necessary, a general knowledge of what a complex Lie algebra is and the main properties of their categories of finite dimensional representations is helpful.