Representation-finite trivial extension algebras

Abstract

Let A be a finite-dimensional basic connected associative algebra over an algebraically closed field, and T(A)=A ⋉ DA its trivial extension by its minimal injective cogenerator. We prove that T( A) is representation-finite of Cartan class Δ if and only if A is an iterated tilted algebra of Dynkin class Δ. The proof also yields a construction procedure for iterated tilted algebras of Dynkin type.