discipline 
Pure
Mathematics

subject 
Representation theory of algebras
2.

lecturers 
István Ágoston 
credits 
2 
period 

curriculum 
Basics of representation theory: directly
indecomposable modules, the theorem of Azumaya–Remak–Krull–Schmidt. Elements
of homological algebra, the Ext functor. Left and
right minimal, left and right almost split morphisms.
Irreducible maps. Almost split (Auslander–Reiten) sequences, their connection to irreducible maps.
The transpose of a module. Projectively or injectively stable module categories. The Auslander–Reiten translate of a
module. The Auslander–Reiten
formulas. Existence of almost split sequences. Irreducible maps for
projective and injective modules. The Auslander–Reiten graph of an algebra, computational examples. Auslander’s proof of the first Brauer–Thrall
Conjecture, the lemma of Harada and Sai. Group
algebras, Higman’s theorem. 
literature 
AuslanderReitenSmalø: Representation Theory of Artin
Algebras 
form of tuition 
Lecture 
mode of assessment 
written/oral
exam 