Displaying similar documents to “From triangulated categories to cluster algebras II”

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

Claire Amiot (2009)

Annales de l’institut Fourier

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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...

Iterated coil enlargements of algebras

Bertha Tomé (1995)

Fundamenta Mathematicae

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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...