Syllabus
The syllabus is based on the videos and lecture notes produced by Øyvind Solberg, which loosely follows the contents of the book "Representation Theory of Artin Algebras" by Auslander–Reiten–Smalø.
Literature
- Authors: M. Auslander, I. Reiten, and S. O. Smalø
- Title: Representation theory of Artin algebras, Cambridge studies in mathematics 36
- Publisher: Cambridge University Press
- Edition: Second edition
- Year: 1995
- ISBN: 0-521-59923-7
- Authors: I. Assem, D. Simson, and A. Skowroński
- Title: Elements of the representation theory of associative algebras, vol 1: techniques of representation theory, London Mathematical Society student textss 65
- Publisher: Cambridge University Press
- Edition: First edition
- Year: 2006
- ISBN: 978-0-521-58631-3
- Authors: A. Skowroński, and K. Yamagata
- Title: Frobenius Algebras I: Basic Representation Theory
- Publisher: European Mathematical Society
- Edition: First edition
- Year: 2011
- ISBN: 978-3-03719-102-6
Overview
Below is an overview of where the topics covered in the video lectures can be found in the books listed above. Parantesis indicates that the topic is covered to a lesser extent than in the course.
| Topic | Video | ARS | ASS | SY |
|---|---|---|---|---|
| Quivers and path algebras | 1 | III.1 p49-51 | II.1 | I.1 |
| Representations of quivers and homomorphisms | 2 | III.1 p51-58 | III | I.2 p21-30 |
| Quivers with relations | 3 | III.1 p58-65 | II.2 | I.2 p26-30 |
| Finite length and Jordan–Hölder | 4 | I.1 | - | I.7 |
| Radicals of rings and modules | 5 | I.3 | I.3 | I.3 |
| Projective modules | 6a-h | I.4 | I.5 | I.8 |
| Krull–Remack–Schmidt for projective modules | 6i-j | I.4 | - | I.4 |
| Krull–Remack–Schmidt | 7 | - | - | I.4 |
| Artin algebras | 8 | II.1 p26-29 | - | - |
| Categories and functors | 9 | II.1 p29- | II.1 | |
| Projectivization | 10 | II.2 | ||
| Basic algebras | 11 | II.2 p35- | (I.6) | II.6 p172-175 |
| Duality | 12 | II.3 | (I.2.9) | II.7 |
| Injective modules | 13 | II.4 |