5 papers
Cluster structures for the singularity
Jenny August, Man-Wai Cheung, Eleonore Faber +2
We study a category of -graded MCM modules over the curve singularity and demonstrate it has infinite type cluster combinatorics. In part…
Cluster tilting modules for mesh algebras
Karin Erdmann, Sira Gratz, Lisa Lamberti
We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid…
Friezes satisfying higher SL-determinants
Karin Baur, Eleonore Faber, Sira Gratz +2
In this article, we construct SL-friezes using Plücker coordinates, making use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of -spaces in…
Conway-Coxeter friezes and mutation: a survey
Karin Baur, Eleonore Faber, Sira Gratz +2
In this survey article we explain the intricate links between Conway-Coxeter friezes and cluster combinatorics. More precisely, we provide a formula, relying solely on the shape of…
Homotopy invariants of singularity categories
Sira Gratz, Greg Stevenson
We present a method for computing -homotopy invariants of singularity categories of rings admitting suitable gradings. Using this we describe any such invariant, e.g.…