2021/01/29 by Sandøy, Mads Hustad, Thibault, Louis-Philippe
#16E30 (Secondary) #16G20 (Primary) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2101.12746
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 \mathbb A3⊗k \mathbb A3, where \mathbb 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.