Mutation in triangulated categories and rigid Cohen–Macaulay modules Page 1 DOI:
10.1007/s00222-007-0096-4 Invent. math. 172, 117–168 (2008) Mutation in triangulated …

The cluster category associated with a finite-dimensional hereditary algebra was introduced
in [21](and in [26] for the An case). It serves in the representation-theoretic approach to …

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 …

CLUSTER ALGEBRAS AND QUANTUM AFFINE ALGEBRAS Page 1 CLUSTER
ALGEBRAS AND QUANTUM AFFINE ALGEBRAS DAVID HERNANDEZ and BERNARD …

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 …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

We show that Derksen–Weyman–Zelevinsky's mutations of quivers with potential yield
equivalences of suitable 3-Calabi–Yau triangulated categories. Our approach is related to …

The first book devoted to cluster algebras, this work contains chapters on Poisson geometry
and Schubert varieties; an introduction to cluster algebras and their main properties; and …

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 …

In the acyclic case, we establish a one-to-one correspondence between the tilting objects of
the cluster category and the clusters of the associated cluster algebra. This correspondence …