Hopf Algebras
Summary
The study of Hopf algebras lies at the interface of representation theory, combinatorial algebra, and mathematical physics. We present an introduction to basic algebraic concepts (coalgebras, bialgebras, Hopf algebras, Hopf modules and comodules, universal enveloping algebras, ...). The highlight of the lecture will be a proof of the Cartier-Kostant theorem for pointed cocommutative Hopf algebras, that describes how a large variety of Hopf algebras are isomorphic to a smash product algebra composed out of the primitive and grouplike elements.
Time and place
We 15-17: Y27-H-26
Th 13-14:45: Y27-H-12
Exercise Sessions
Tu 10:15-12: Y27-H-46 with Raúl Penaguião
Lecture notes
The lecture notes summarize the material covered in class and will be updated throughout the semester.
Homework
- Exercise Sheet 01, Solutions Sheet 01
- Exercise Sheet 02, Solutions Sheet 02
- Exercise Sheet 03, Solutions Sheet 03
- Exercise Sheet 04, Solutions Sheet 04
- Exercise Sheet 05, Solutions Sheet 05
- Exercise Sheet 06, Solutions Sheet 06
- Exercise Sheet 07, Solutions Sheet 07
- Exercise Sheet 08, Solutions Sheet 08
Links and Information
- [06.03.2018] What is... a quantum group - a talk by Artem Kalmykov at the Zurich Graduate Colloqium.