Concealed-Canonical Algebras and Separating Tubular Families

Abstract

We characterise those concealed-canonical algebras which arise as endomorphism rings of tilting modules, all of whose indecomposable summands have strictly positive rank, as those artin algebras whose module categories have a separating exact subcategory (that is, a separating tubular family of standard tubes). This paper develops further the technique of shift automorphisms which arises from the tubular structure. It is related to the characterisation of hereditary noetherian categories with a tilting object as the categories of coherent sheaves on a weighted projective line.