EUDML

We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field $k$ . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category $𝒯$ is of the form $ℤ Δ / G$ where $Δ$ is a disjoint union of simply-laced Dynkin diagrams and $G$ a weakly admissible group of automorphisms of $ℤ Δ$ . Then we prove that for ‘most’ groups $G$ , the category $𝒯$ is standard, ...

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

Claire Amiot — 2009

Annales de l’institut Fourier

Let $k$ be a field and $A$ a finite-dimensional $k$ -algebra of global dimension $\leq 2$ . 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 results also...

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Discussion des valeurs générales fournies par la résolution de trois équations du premier degré entre trois inconnues

Sur l'approximation des calculs numériques par les décimales

Sur la détermination d'une courbe du 2e ordre, donnée par son équation

Mémoire sur les polygones réguliers

Note sur quelques points de la théorie analytique des surfaces.

Mémoire sur les diverses propriétés des surfaces du deuxième ordre déduites de la théorie des focales.

Mémoire sur une nouvelle méthode de génération et de discussion des surfaces du deuxième ordre.

On the structure of triangulated categories with finitely many indecomposables

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