13 citations · 20 across the 5 of their papers we have counts for
10 papers
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…
The bar automorphism in quantum groups and geometry of quiver representations
Philippe Caldero, Markus Reineke
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over fin…
Rational smoothness of varieties of representations for quivers of Dynkin type
Philippe Caldero, Ralf Schiffler
With the help of Lusztig's canonical basis, we study local intersection cohomology of the Zariski closures of orbits of representations of a quiver of type A, D or E. In particular…
Adapted algebras and standard monomials
Philippe Caldero, Peter Littelmann
Let G be a complex semisimple Lie group. The aim of this article is to compare two basis for G-modules, namely the standard monomial basis and the dual canonical basis. In particul…