Representation Theory of Algebras

The content can vary, but there will be a core containing algebras given by quiver, representations of quivers, almost split sequences, Brauer Thrall 1, classification of hereditary algebras of finite type, functor categories, tilting theory for artin algebras.

1. Knowledge The content may vary, but there will be a core containing the following: Algebras given by quivers, almost split sequences, irreducible maps, AR-quivers, Auslander algebras and their homological characterization, hereditary algebras of finite type, functor categories, tilting theory. Also the following special classes of algebras will be discussed : selfinjective, symmetric, Nakayama. 2. Skills The students should be learn the representation theory for algebras and be able to conduct researches in representation theory for algebras and its applications. 3. Competence The students should be able to participate in scientific discussions and begin with own reseach in representation theory.

Lectures, alternatively guided self-studiy.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.