On preprojective and preinjective partitions of a \(\Delta\)-good module category.
Let \(\Lambda\) be a quasi-hereditary algebra. Then the category \({\mathcal F}(\Delta)\) of modules with a \(\Delta\)-filtration is functorially finite [see \textit{C. M. Ringel}, Math. Z. 208, No. 2, 209--224 (1991; Zbl 0725.16011)] and thus it has preprojective and preinjective partitions. For module categories, \textit{A. Skowroński} and \textit{S. O. Smalø} [see Arch. Math. 64, No. 1, 8--10 (1995; Zbl 0813.16007)] have shown that finite representation type is equivalent to every indecomposable module being preprojective or preinjective. An analogue of this result is shown in the present article for the category \({\mathcal F}(\Delta)\). On the way to the final result, the author studies components of the Auslander-Reiten quiver and degrees of irreducible maps. She transfers a variety of useful technology from module categories to the category \({\mathcal F}(\Delta)\). She also uses the validity of Brauer-Thrall II for certain bimodule problems.
scientific article; zbMATH DE number 2157750
scientific article