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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
9 Radical: Top and Socle Basic algebras: definition Exercise session 5
10 Basic algebras: quiver of a basic algebra Basic algebras: Morita equivalence Exercise session 6
11 Projective and injective modules: definitions Projective and injective modules: essential epimorphism Exercise session 7
12 Projective and injective modules: representation of quivers Projective and injective modules: projective cover
13 Duality: definition and properties Duality: Nakayama functor Exercise session 8
14 Categories: projective resolutions, Ext functor Quivers: Extensions between simples Exercise session 9 Tuesday April 2 lecture in R60
15 Krull-Remak-Schmidt theorem: Fitting lemma Krull-Remak-Schmidt theorem Exercise session 10
16 No Lecture No Lecture
17 No Lecture Exercise session and questions Exercise session 11
2019-02-14, louispht