Algebras of Finite Representation Type

Abstract

In this thesis we are considering finite dimensional algebras. We prove that any basic and indecomposable finite dimensional algebra A over an algebraically closed field k is isomorphic to a bound quiver algebra. Furthermore, if A is hereditary we prove that it is isomorphic to a path algebra. Finally, we prove that a path algebra is of finite representation type if and only if the underlying graph of the quiver is a Dynkin diagram. This is done using reflection functors.