We prove that in a 2-Calabi–Yau triangulated category, each cluster tilting subcategory is
Gorenstein with all its finitely generated projectives of injective dimension at most one. We …

We investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and
related categories. In particular, we construct a new class of such categories related to …

Cluster algebras were invented by Fomin and Zelevinsky in 2001 [9]. One of the main
motivations for introducing this new class of commutative algebras was to provide a …

The cluster category is a triangulated category introduced for its combinatorial similarities
with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a …

Let Q be a finite quiver without oriented cycles, let Λ be the associated preprojective algebra,
let g be the associated Kac–Moody Lie algebra with Weyl group W, and let n be the positive …

Cluster algebras were invented and studied by S. Fomin and A. Zelevinsky in [12],[13],[11]
and in collaboration with A. Berenstein in [1]. They are commutative algebras endowed with …

We show that the quantum coordinate ring of the unipotent subgroup N (w) of a symmetric
Kac–Moody group G associated with a Weyl group element w has the structure of a quantum …

Abstract We study support\(\tau\)-tilting modules over preprojective algebras of Dynkin type.
We classify basic support\(\tau\)-tilting modules by giving a bijection with elements in the …

Partial flag varieties and preprojective algebras Page 1 ANNA L E S D E L’INSTITU T FO U
RIER ANNALES DE L’INSTITUT FOURIER Christof GEISS, Bernard LECLERC & Jan …

We prove a structure theorem for triangulated Calabi–Yau categories: an algebraic 2-Calabi–
Yau triangulated category over an algebraically closed field is a cluster category if and only …