177 citations · 1.7k across the 51 of their papers we have counts for
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Rigid modules and Schur roots
Christof Geiß, Bernard Leclerc, Jan Schröer
Let be a symmetrizable generalized Cartan matrix with symmetrizer and orientation . In previous work we associated an algebra to this data, such that the locally fre…
Quantum cluster algebras and their specializations
Christof Geiß, Bernard Leclerc, Jan Schröer
We show that in case a cluster algebra coincides with its upper cluster algebra and the cluster algebra admits a grading with finite dimensional homogeneous components, the corresp…
Quivers with relations for symmetrizable Cartan matrices V. Caldero-Chapoton formula
Christof Geiß, Bernard Leclerc, Jan Schröer
We generalize the Caldero-Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers…
Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions
Christof Geiß, Bernard Leclerc, Jan Schröer
We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semi…
Quivers with relations for symmetrizable Cartan matrices III: Convolution algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
We realize the enveloping algebra of the positive part of a semisimple complex Lie algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-G…
Quivers with relations for symmetrizable Cartan matrices II: Change of symmetrizers
Christof Geiss, Bernard Leclerc, Jan Schröer
For we consider the -algebra associated to a symmetrizable Cartan matrix , a symmetrizer , and an orientation of , which was defined i…