**Introduction to Hopf algebras (Spring 2023)**

**Note:** A version of this course will run as an SMSTC Supplementary Module in 2023-4 during Semester 2; further information will be available through the SMSTC web site. All staff and PhD students will be welcome to attend the Zoom lectures.

The aim is to cover basic notions of Hopf algebras, their modules and comodules, results on finite dimensional Hopf algebras, etc.

Andy Baker (andrew.j.baker@glasgow.ac.uk)

**Very rough outline**

I will assume a basic exposure to category theory although a lot will crop up and can be discussed later; there are some minimalist notes on this here. I will also assume that students are aware of tensor products of vector spaces, etc, but the Notes contain a sketchy introduction to the background material needed.

Lecture 1 (11/01/2023)

Algebras and coalgebras over a field

Lecture 2 (18/01/2023)

Bialgebras and Hopf algebras

Lecture 3 (25/01/2023)

Lots of examples. You are encouraged to have a look at the examples in the notes yourself. Lewis and Parth will discuss enveloping algebras for Lie algebras and affine group schemes.

Lecture 4 (01/02/2023)

SubHopf algebras, adjoint actions and normal subalgebras

Lecture 5 (08/02/2023)

Modules and comodules, representation theory

of a Hopf algebra

Lectures 6 & 7 (15/02/2023 & 22/02/2023)

Hopf modules and finite dimensional Hopf algebras

Lectures 8 & 9 (01/03/2023 & 08/03/2023)

Quantum Groups