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Lecture plan and exercises
This is a tentative schedule for the course.
Exercises will be posted here every week. You will be expected to have worked on them before the next exercise session, which will be held in class during the last hour of the Friday lecture.
| Week | Tuesday | Friday | Exercises | Remarks |
|---|---|---|---|---|
| 2 | Introduction | Quivers and path algebras: definitions | Friday January 11 lecture in 656 | |
| 3 | Categories: definitions, functors. Representation of quivers: definition. | Categories: natural transformations, equivalences of categories. Representation of quivers: morphisms between representations. | ||
| 4 | Representation of quivers: Equivalence between Rep_k(Q) and Mod kQ. | Representation of quivers: subrepresentations, quotient, indecomposable representations | Exercise session 1 | |
| 5 | Representation of quivers: Classifying indecomposables, matrix problems, finite and tame representation type | Representation of quivers: wild representation type | Exercise session 2 | Tuesday January 29 lecture in R60, Friday Feb. 1st lecture in 656 |
| 6 | Length of a module: composition series, short exact sequences | Length of a module: short exact sequences | Exercise session 3 | |
| 7 | Length of a module: Jordan-Hölder theorem, links with artinian and noetherian modules | Radical: definition, Nakayama lemma | Exercise session 4 with Hints | Not every PDF reader seems to work to see the hints. Adobe Acrobate Reader certainly does. |
| 8 | Radical: links with left artinian rings, Radical of a module | Quivers and path algebras: admissible ideals, representation of bound quivers, radical of a path algebra | Exercise session 5 | |
| 9 | Radical: Top and Socle | Basic algebras: definition | Exercise session 6 | |
| 10 | Basic algebras: quiver of a basic algebra | Basic algebras: Morita equivalence | Exercise session 7 | |
| 11 | Projective and injective modules: definitions | Projective and injective modules: essential epimorphism | Exercise session 8 | |
| 12 | Projective and injective modules: representation of quivers | Projective and injective modules: projective cover | Exercise session 9 | |
| 13 | Duality: definition and properties | Duality: Nakayama functor | Exercise session 10 | |
| 14 | Categories: projective resolutions, Ext functor | Quivers: Extensions between simples | Exercise session 11 | Tuesday April 2 lecture in R60 |
| 15 | Krull-Remak-Schmidt theorem: Fitting lemma | Krull-Remak-Schmidt theorem | Exercise session 12 | |
| 16 | No Lecture | No Lecture | ||
| 17 | No Lecture | Exercise session and questions | Exercise session 13 |