A simple homological characterization of string algebras of finite representation type

MARIANO SUÁREZ-ALVAREZ

Conferencia; VIRTUAL ARTA 2021 Advances in Representation Theory of Algebras; 2021

We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at most two direct factors. On the other hand, we show that non-domestic string algebras are very far from having that property.