Valentine Soto

Path algebras with relations appear naturally in the representation theory of finite dimensional algebras. These algebras are constructed thanks to an oriented graph called a quiver. The goal of this talk is to present a result by Gabriel which gives an isomorphism between finite dimensional algebras and these path algebras under some conditions. First, I will explain how one can construct a finite dimensional algebra from the data of a quiver. Conversely, I will explain how one can naturally associate a quiver to any finite dimensional algebra.