Displaying similar documents to “Irreducible morphisms, the Gabriel-valued quiver and colocalizations for coalgebras.”

Cluster categories for algebras of global dimension 2 and quivers with potential

Claire Amiot (2009)

Annales de l’institut Fourier

Similarity:

Let k be a field and A a finite-dimensional k -algebra of global dimension ≤ 2 . We construct a triangulated category 𝒞 A associated to A which, if  A is hereditary, is triangle equivalent to the cluster category of A . When 𝒞 A is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our...

Quasitilted algebras have preprojective components

Ole Enge (2000)

Colloquium Mathematicae

Similarity:

We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.

Slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2007)

Open Mathematics

Similarity:

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.