177 citations · 1.4k across the 38 of their papers we have counts for
35 papers · 1 filter
Minimal presentations of finite-dimensional representations of pseudocompact algebras
Christof Geiss, Carolin Hartung, Daniel Labardini-Fragoso +1
We give a general formula for minimal projective presentations and for minimal discrete-injective presentations of finite-dimensional modules over basic pseudocompact algebras. We…
Bangle functions are the generic basis for cluster algebras from punctured surfaces with boundary
Christof Geiß, Daniel Labardini-Fragoso, Jon Wilson
We prove that for any possibly-punctured surface with non-empty boundary , and any tagged triangulation of in the sense of Fomi…
Laminations of punctured surfaces as -regular irreducible components
Christof Geiß, Daniel Labardini-Fragoso, Jon Wilson
Let be a surface with marked points on the boundary, and punctures $\mathbb{P}\subsetΣ\setminu…
On homomorphisms and generically -regular components for skewed-gentle algebras
Christof Geiß
Let be an algebraically closed field with , and a skewed-gentle -algebra. In this case, Crawley-Boevey's description of the indecomposable…
A geometric construction of for affine Kac-Moody algebras of type
Alberto Castillo Gómez, Christof Geiss
Inspired by the work of Geiss, Leclerc and Schröer [Represent. Theory 20, (2016)] we realize the enveloping algebra of the positive part of an affine Kac-Moody Lie algebra of Dynki…
Semicontinuous maps on module varieties
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that -v…
A model for the canonical algebras of bimodules type (1, 4) over truncated polynomial rings
Christof Geiß, David Reynoso-Mercado
Let be the field of complex Laurent series. We use Galois descent techniques to show that the simple regular representations of the species of type $(1,\, 4…
Generic Caldero-Chapoton functions with coefficients and applications to surface cluster algebras
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We realize Derksen-Weyman-Zelevinsky's mutations of representations as densely-defined regular maps on representation spaces, and study the generic values of Caldero-Chapoton funct…
Schemes of modules over gentle algebras and laminations of surfaces
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of…
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 and algebraic Lie theory
Christof Geiß
We give an overview of our effort to introduce (dual) semicanonical bases in the setting of symmetrizable Cartan matrices.
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…
Quivers with relations for symmetrizable Cartan matrices II : Convolution algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
We realize the enveloping algebra of the positive part of a symmetrizable Kac-Moody algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-…
Quivers with relations for symmetrizable Cartan matrices I : Foundations
Christof Geiss, Bernard Leclerc, Jan Schröer
We introduce and study a class of Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path a…
The representation type of Jacobian algebras
Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
We show that the representation type of the Jacobian algebra P(Q,S) associated to a 2-acyclic quiver Q with non-degenerate potential S is invariant under QP-mutations. We prove tha…
A Caldero-Chapoton formula for generalized Cluster Categories
Salomón Dominguez, Christof Geiss
The Caldero-Chapoton formula relates for hereditary algebras of Dynkin type the cluster characters of the end terms of an Auslander-Reiten sequence with the cluster character of th…
Cluster algebras in algebraic Lie theory
Christof Geiss, Bernard Leclerc, Jan Schröer
We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized ver…
Tubular Cluster Algebras II: Exponential growth
Michael Barot, Christof Geiss, Gustavo Jasso
Among the mutation finite cluster algebras the tubular ones are a particularly interesting class. We show that all tubular (simply laced) cluster algebras are of exponential growth…
Generic bases for cluster algebras and the Chamber Ansatz
Christof Geiß, Bernard Leclerc, Jan Schröer
Let Q be a finite quiver without oriented cycles, and let be the corresponding preprojective algebra. Let g be the Kac-Moody Lie algebra with Cartan datum given by Q, and let W…
Kac-Moody groups and cluster algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
Let Q be a finite quiver without oriented cycles, let Λbe the associated preprojective algebra, let g be the associated Kac-Moody Lie algebra with Weyl group W, and let n be the po…