Quivers and representations

lecture series by
Raquel Coelho Simoes
Lancaster University

March 14-25, 2022

In this lecture series, we will consider representation theory of finite dimensional algebras, which can be reduced to the study of representations over quotients of algebras generated by paths of a quiver. We will give an introduction to Auslander-Reiten theory, which gives us a way to visualise the representation theory of a finite dimensional algebra using a quiver, called the Auslander-Reiten quiver, where the vertices and the arrows correspond to the “building blocks” of the modules over the algebra (i.e. indecomposable modules) and of the morphisms between them (i.e. irreducible morphisms), respectively.