Lecture 16: Representations of Quivers

Now we proceed to study representations of quivers. We start by recalling some basic definitions and constructions such as the path algebra and indecomposable representations. Then we state a theorem of Kac that describes the dimensions, where the indecomposable representations occur as well as the number of parameters needed to describe their isomorphism classes. We will prove the Kac theorem only partially using Crawley-Boevey’s approach based on deformed preprojective algebras. This approach does not allow to prove Kac’s theorem completely but it is more elementary than Kac’s original approach.