Directing components for quasitilted algebras
We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
A note on tilting sequences
We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
On Auslander–Reiten components for quasitilted algebras
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander-Reiten quiver of a quasitilted algebra A.
Limits of tilting modules
We study the problem of when a direct limit of tilting modules is still a tilting module.
On minimal non-tilted algebras
A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
Strongly simply connected coil algebras
We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.
Page 1