17 citations · 67 across the 17 of their papers we have counts for
14 papers · 1 filter
On Maximal Green Sequences
Thomas Brüstle, Grégoire Dupont, Matthieu Pérotin
Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maxima…
Modules over cluster-tilted algebras determined by their dimension vectors
Ibrahim Assem, Grégoire Dupont
We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed al…
On a category of cluster algebras
Ibrahim Assem, Grégoire Dupont, Ralf Schiffler
We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characte…
Generic Variables in Acyclic Cluster Algebras
Gregoire Dupont
Let be an acyclic quiver. We introduce the notion of generic variables for the coefficient-free acyclic cluster algebra . We prove that the set o…
A homological interpretation of the transverse quiver Grassmannians
Giovanni Cerulli Irelli, Gregoire Dupont, Francesco Esposito
In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver G…
Friezes and a construction of the euclidean cluster variables
I. Assem, G. Dupont
Let be an euclidean quiver. Using friezes in the sense of Assem-Reutenauer-Smith, we provide an algorithm for computing the (canonical) cluster character associated to any obje…
Generic cluster characters
G. Dupont
Let $\CC$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster-tilting object . Under a constructibility condition we prove the existence of a set $\mathcal G^T(\CC…
Positivity for Regular Cluster Characters in Acyclic Cluster Algebras
G. Dupont
Let be an acyclic quiver and let be the corresponding cluster algebra. Let be the path algebra of over an algebraically closed field and let be an i…
Transverse Quiver Grassmannians and Bases in Affine Cluster Algebras
Gregoire Dupont
Sherman-Zelevinsky and Cerulli constructed canonically positive bases in cluster algebras associated to affine quivers having at most three vertices. Both constructions involve clu…
Quantized Chebyshev polynomials and cluster characters with coefficients
G. Dupont
We introduce quantized Chebyshev polynomials as deformations of generalized Chebyshev polynomials previously introduced by the author in the context of acyclic coefficient-free clu…
Generic Variables in Acyclic Cluster Algebras and Bases in Affine Cluster Algebras
G. Dupont
Let be a finite quiver without oriented cycles and be the coefficient-free cluster algebra with initial seed . Using the Caldero-Chapoton map, we…
Cluster multiplication in regular components via generalized Chebyshev polynomials
G. Dupont
We introduce a multivariate generalization of normalized Chebyshev polynomials of the second kind. We prove that these polynomials arise in the context of cluster characters associ…
Caldero-Keller approach to the denominators of cluster variables
G. Dupont
Buan, Marsh and Reiten proved that if a cluster-tilting object in a cluster category associated to an acyclic quiver satisfies certain conditions with respect…
An approach to non simply laced cluster algebras
G. Dupont
Let be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra…