A simple homological characterization of string algebras of finite representation type (Q6070274)

\textit{I. M. Gel'fand} and \textit{V. A. Ponomarev} [Russ. Math. Surv. 23, No. 2, 1--58 (1968; Zbl 0236.22012); translation from Usp. Mat. Nauk 23, No. 2 (140), 3--60 (1968)] made the observation that the representation theory of the Lorentz group is closely related to that of a certain algebra, and used this to show that the group has tame representation type and to describe explicitly its finite-dimensional indecomposable modules. Soon afterwards, the class of finite-dimensional algebras to which the same techniques can be applied was identified. M. Suarez-Álvarez proves 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, the author shows that non-domestic string algebras are very far from having that property.