Quivers, Algebras and Representations (150270-WiSe 2024/25)

In the first part of this course, we will study algebras and categories of modules. Then we will see how algebras can be described using quivers (oriented graphs), by an important result of Gabriel. This leads us to consider representations of quivers: a representation of a quiver is a collections of vector spaces and linear maps for the given quiver. In order to describe a category of modules (or of representations) we will study indecomposable objects and decompositions into them. This leads us to Auslander-Reiten theory.