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 AzumayaRemakKrull–Schmidt. Elements of homological algebra, the Ext functor. Left and right minimal, left and right almost split morphisms. Irreducible maps. Almost split (AuslanderReiten) sequences, their connection to irreducible maps. The transpose of a module. Projectively or injectively stable module categories. The AuslanderReiten translate of a module. The AuslanderReiten formulas. Existence of almost split sequences. Irreducible maps for projective and injective modules. The AuslanderReiten 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

Auslander-Reiten-Smalø: Representation Theory of Artin Algebras

form of tuition

Lecture

mode of assessment

written/oral exam