The course is an introduction to representation theory of finite-dimensional algebras. Our main goal is to get close to Auslander-Reiten theory

1. Modules of finite length. Jordan-Hölder Theorem.
2. Simple and indecomposable modules. Krull-Schmidt Theorem.
3. Radical. Jacobson radical. Semisimplicity.
4. Projective modules and projective covers.
5. Semisimple algebras. Artin-Wedderburn Theorem.
6. Quivers, path algebras, representations of quivers.
7. Projective dimension. Hereditary algebras.
8. Morita equivalence.
9. Algebras of finite type. Gabriel’s Theorem.
10. Introduction to to Auslander-Reiten theory.

Lecturer
Fonarev Anton Vyacheslavovich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center