242 citations · 272 across the 16 of their papers we have counts for
16 papers
On the quiver Grassmannian in the acyclic case
Philippe Caldero, Markus Reineke
Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain som…
Laurent expansions in cluster algebras via quiver representations
Philippe Caldero, Andrei Zelevinsky
We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtai…
From triangulated categories to cluster algebras II
Philippe Caldero, Bernhard Keller
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 correspon…
From triangulated categories to cluster algebras
Philippe Caldero, Bernhard Keller
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 realize…
Quivers with relations and cluster tilted algebras
Philippe Caldero, Frederic Chapoton, Ralf Schiffler
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the clust…
Cluster algebras as Hall algebras of quiver representations
Philippe Caldero, Frederic Chapoton
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type…