Representation Theory of Finite Groups and Associative Algebras, Math 423/502, January-April 2016
- Instructor: Rachel Ollivier
- Email: email@example.com
- Time and Location: MWF 1pm-1:50pm in Math Building 102
- Office hours: Wednesday and Friday at 11am-12pm in Math Building 235
- Homework and Syllabus: Please check here for the tentative syllabus.
- Grading: Midterms 25% each, Homework 50%. I'll ask you to submit a certain number of problems from this list (this file will be updated regularly). The due date will be decided later.
- Midterm dates: see the syllabus.
- This class is an introduction to the representation theory of finite groups and associative algebras.
We will start with representations of associative algebras
(irreducible and indecomposable representations, Schur's
lemma...), then move on to the representation theory of finite groups
over the complex numbers (theory of characters, Mashke's theorem,
induction of representations, Mackey's formula...). Via concrete examples, we will compare the
representations of a finite group G over the complex numbers to
the representations of G over a field with positive
characteristic. To be able to expand on these examples in a more
abstract way, we will then introduce some notions of homological
algebra (categories, exact functors, projectives, injectives).
- There are a lot of references on
representation theory of finite groups. A classical one is the book of
Serre, Linear Representations of Finite Groups. However, it is not
necessary to own a book as there are many online resources: an online book by P.Webb, notes by D.M. Jackson, etc.
Any reference about modules can be useful too (your own course notes
from another class, or the corresponding chapter of any algebra book
such as Dummit and Foote).
Other references will be added for specific topics throughout the semester.