Hopf Algebras
Content
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Description
Time: Thursdays 11.00 - 13.00
Location for Maxwell Institute students: Bayes Centre (room 5.46)
Module Leader: Andrew Baker (University of Glasgow)
Nowadays Hopf algebras are ubiquitous in many parts of mathematics. This course will introduce the main ideas by studying Hopf algebras over fields, and it should be of particular interest to people working in areas such as algebra, algebraic geometry, representation theory and algebraic/geometric topology. The development of the subject requires familiarity with many category theory notions (e.g., functors, adjunctions, monoidal categories) and these will be introduced as required.
Students are encouraged to read recommended books to fill in gaps and obtain deeper understanding of the material and are also encouraged to offer talks on topics of their choosing based on the notes or other sources. To obtain credit for the course students will be required to give at least one talk.
Introductory talk at Perth Symposium
Lecture Notes: these will appear here and be updated regularly Note that the current version is from 2024-5 and is not intended to be downloaded.
Outline of material covered in lectures (with source in notes)
- Background material on category theory and vector spaces (Chapter 1)
- Algebras, coalgebras and bialgebras (Chapter 2)
- Convolution monoids and Hopf algebras (Chapter 2)
- Examples (Chapter 3)
- Modules and comodules (Chapter 4)
- Modules and comodules over Hopf algebras (Chapter 4)
The notes contain a list of books and other source material.
Other sources
Category Theory in Context by Emily Riehl
Notes by J. Kock on Frobenius Algebras (this is a cut down version of his book)
Assessment
Details TBC