Glueings of tilted algebras

AbstractLet A be a basic connected finite-dimensional algebra over an algebraically closed field. We show that if A has all its indecomposable projectives (or injectives) lying in a component of the Auslander—Reiten quiver consisting entirely of postprojective (or preinjective, respectively) modules in the sense of Auslander and Smalø then A is a finite enlargement in the postprojective (or preinjective, respectively) components of a finite set of tilted algebras having complete slices in these components. We call such an algebra A a left (or right, respectively) glued algebra and study some of its homological properties in particular in the case where A is itself a tilted algebra