Finite Versus Infinite Dimensional Representations — A New Definition of Tameness

Abstract

Let Λ be a finite dimensional algebra over some algebraically closed field k. In this note I discuss the relationship between finite and infinite dimensional modules over Λ. This discussion is based on the following three fundamental concepts: fp-idempotent ideals in the category mod Λ of finite dimensional Λ-modules endofinite modules in the category Mod Λ of all Λ-modules coherent functors Mod Γ→ Mod Λ between two module categories