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Representation Theory course material

This is the course home page for the Representation Theory module for the London Taught Course Centre for Phd students in mathematics.

Syllabus

This module is an introduction to results from classical and modern representation theory concentrating mostly on finite dimensional algebras.

1. Algebras and modules
Basic definitions and examples (including group algebras, quivers).

2. Semisimplicity and some basic structure theorems
Including Maschke's theorem and classical results such as Krull-Schmidt.

3. Projective and injective modules
Basic definitions and examples.

4. Categories and functors
Basic definitions and examples.

5. Representation type and Gabriel's theorem
An application to quivers of the theory so far.

6. Further directions
A brief survey of related topics in modern representation theory.

Handouts

Handouts for the course will appear here.

• Introduction
• Week 1
• Week 2
• Week 3
• Week 4
• Week 5

Books

There are a few books which correspond loosely to the material in the course, though none are a substitute for attending the lectures. The first volume below will be used to supplement the lectures, the others are a little more advanced.

• Assem, Simson, and Skowroński: Elements of the representation theory of associative algebras: Vol 1 LMS student text 65 (CUP)
• Auslander, Reiten, and Smalø: Representation theory of Artin algebras (CUP)
• Gabriel and Roiter: Representation theory of finite-dimensional algebras (Springer)

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Anton Cox (A.G.Cox@city.ac.uk)
Last Modified: Mon 29 Oct 2012