177 citations · 1.7k across the 51 of their papers we have counts for
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Factorial cluster algebras
Christof Geiß, Bernard Leclerc, Jan Schröer
We show that cluster algebras do not contain non-trivial units and that all cluster variables are irreducible elements. Both statements follow from Fomin and Zelevinsky's Laurent p…
Quantum Grothendieck rings and derived Hall algebras
David Hernandez, Bernard Leclerc
We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite…
Cluster structures on quantum coordinate rings
C. Geiss, B. Leclerc, J. Schröer
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 clust…
Quantum loop algebras, quiver varieties, and cluster algebras
Bernard Leclerc
These notes reflect the contents of three lectures given at the workshop of the 14th International Conference on Representations of Algebras (ICRA XIV), held in August 2010 in Toky…