On \(\Delta\)-good module categories of quasi-hereditary algebras
Let \(A\) be a quasi-hereditary algebra. Denote by \({\mathcal F}(\Delta)\) the category of \(A\)-modules which have a filtration by standard modules. The authors study the question whether \({\mathcal F}(\Delta)\) has finite type, that is, whether it has only finitely many indecomposable objects up to isomorphism. They reformulate the problem in terms of vector space categories. Using Kleiner's list of representation finite posets, they then solve the problem for a quite special class of quasi-hereditary algebras, which are obtained from certain posets by sort of a doubling process.
scientific article; zbMATH DE number 1112257