# 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.

#### 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)

Anton Cox
(A.G.Cox@city.ac.uk)

Last Modified: Mon 29 Oct 2012