Classification results for n-hereditary monomial algebras

Abstract

We classify n-hereditary monomial algebras in three natural contexts: First, we give a classification of the n-hereditary truncated path algebras. We show that they are exactly the n-representation-finite Nakayama algebras classified by Vaso. Next, we classify partially the n-hereditary quadratic monomial algebras. In the case n=2, we prove that there are only two examples, provided that the preprojective algebra is a planar quiver with potential. The first one is a Nakayama algebra and the second one is obtained by mutating kA3⊗kkA3, where A3 is the Dynkin quiver of type A with bipartite orientation. In the case n≥3, we show that the only n-representation finite algebras are the n-representation-finite Nakayama algebras with quadratic relations.