Cluster algebras are a class of commutative rings endowed with an additional combinatorial
structure, which involves a set of distinguished generators (cluster variables) grouped into …

arXiv:math/0601185v5 [math.KT] 19 Jun 2006 Page 1 arXiv:math/0601185v5 [math.KT] 19 Jun
2006 ON DIFFERENTIAL GRADED CATEGORIES BERNHARD KELLER Abstract. Differential …

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 …

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 …

Let Λ be a preprojective algebra of simply laced Dynkin type Δ. We study maximal rigid Λ-
modules, their endomorphism algebras and a mutation operation on these modules. This …

We prove that the quantum cluster algebra structure of a unipotent quantum coordinate ring
$ A_q (\mathfrak {n}(w)) $, associated with a symmetric Kac–Moody algebra and its Weyl …

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 …

We define and study category $\mathcal O $ for a symplectic resolution, generalizing the
classical BGG category $\mathcal O $, which is associated with the Springer resolution. This …