We study quivers with relations given by noncommutative analogs of Jacobian ideals in the
complete path algebra. This framework allows us to give a representation-theoretic …

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 …

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 …

For any cluster algebra whose underlying combinatorial data can be encoded by a bordered
surface with marked points, we construct a geometric realization in terms of suitable …

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 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 …

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 …

Abstract We introduce (n+ 1)-preprojective algebras of algebras of global dimension n. We
show that if an algebra is n-representation-finite then its (n+ 1)-preprojective algebra is self …