177 citations · 1k across the 25 of their papers we have counts for
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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…
-symmetric algebras I
Grzegorz Bobiński, Jan Schröer
We study various symmetry conditions related to the Auslander-Reiten formula for finite-dimensional algebras. In particular, we define a new class of algebras which we call -sym…
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…
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…
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 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…
Caldero-Chapoton algebras
Giovanni Cerulli Irelli, Daniel Labardini-Fragoso, Jan Schröer
Motivated by the representation theory of quivers with potentials introduced by Derksen, Weyman and Zelevinsky and by work of Caldero and Chapoton, who gave explicit formulae for t…
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…
Preprojective algebras and cluster algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
Cluster algebra structures and semicanonical bases for unipotent groups
Christof Geiss, Bernard Leclerc, Jan Schröer
Let Q be a finite quiver without oriented cycles, and let be the associated preprojective algebra. To each terminal representation M of Q (these are certain preinjective repres…
Partial flag varieties and preprojective algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
Let L be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories sub(Q)…
Semicanonical bases and preprojective algebras II: A multiplication formula
Christof Geiß, Bernard Leclerc, Jan Schröer
Let be a maximal nilpotent subalgebra of a complex symmetric Kac-Moody Lie algebra. Lusztig has introduced a basis of U(n) called the semicanonical basis, whose elements can be…
Auslander algebras and initial seeds for cluster algebras
Christof Geiß, Bernard Leclerc, Jan Schröer
Let be a Dynkin quiver and the corresponding set of positive roots. For the preprojective algebra associated to we produce a rigid -module with pai…
Rigid modules over preprojective algebras
Christof Geiß, Bernard Leclerc, Jan Schröer
Let $\la$ be a preprojective algebra of simply laced Dynkin type . We study maximal rigid $\la$-modules, their endomorphism algebras and a mutation operation on these modules. T…
Verma modules and preprojective algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
We give a geometric construction of the Verma modules of a symmetric Kac-Moody Lie algebra in terms of constructible functions on the varieties of nilpotent finite-dimensional modu…
Semicanonical bases and preprojective algebras
Christof Geiss, Bernard Leclerc, Jan Schröer
We study the multiplicative properties of the dual of Lusztig's semicanonical basis.The elements of this basis are naturally indexed by theirreducible components of Lusztig's nilpo…
Extension-orthogonal components of nilpotent varieties
Christof Geiß, Jan Schröer
Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-m…
Stable endomorphism algebras of modules over special biserial algebras
Jan Schröer, Alexander Zimmermann
We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial.…