16 citations · 32 across the 18 of their papers we have counts for
23 papers
Ore's theorem for thick subcategories
Sira Gratz, Greg Stevenson
We characterize those finite groups for which the bounded derived category of finite dimensional representations over an algebraically closed field of characteristic has distri…
An equivalence linking CM-types and
Charley Cummings, Sira Gratz, Ellen Kirkman +3
We show that, for a specific grading, the stable categories of graded maximal Cohen-Macaulay modules over hypersurfaces of type and are equivalent.
Abstract Cluster Structures
Jan E. Grabowski, Sira Gratz
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster m…
Ind-cluster algebras and infinite Grassmannians
Sira Gratz, Christian Korff
A prototypical examples of a cluster algebra is the coordinate ring of a finite Grassmannian: using the Plücker embedding the cluster algebra structure allows one to move between `…
Tilting in -shaped derived categories
Sira Gratz, Henrik Holm, Peter Jorgensen +1
The main result of this paper is that there is sometimes a triangulated equivalence between , the -shaped derived category of an algebra , and , the classic…
Metric completions of discrete cluster categories
Charley Cummings, Sira Gratz
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with…
Homotopy Invariants for gradable finite dimensional algebras
Sira Gratz, Theo Raedschelders, Špela Špenko +1
We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.
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…
Approximating triangulated categories by spaces
Sira Gratz, Greg Stevenson
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the var…
Lattices of t-structures and thick subcategories for discrete cluster categories
Sira Gratz, Alexandra Zvonareva
We classify t-structures and thick subcategories in discrete cluster categories of Dynkin type , and show that the set of all t-structures on $\mathca…
Categories for Grassmannian cluster algebras of infinite rank
Jenny August, Man-Wai Cheung, Eleonore Faber +2
We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian c…
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.…
Cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type
Sira Gratz, Thorsten Holm, Peter Jorgensen
We give a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type .
Mutation of friezes
Karin Baur, Eleonore Faber, Sira Gratz +2
We study mutations of Conway-Coxeter friezes which are compatible with mutations of cluster-tilting objects in the associated cluster category of Dynkin type . More precisely, w…
On the graded dual numbers, arcs, and non-crossing partitions of the integers
Sira Gratz, Greg Stevenson
We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this mod…
Transfinite mutations in the completed infinity-gon
Karin Baur, Sira Gratz
We introduce mutation along infinite admissible sequences for infinitely marked surfaces, that is surfaces with infinitely many marked points on the boundary. We show that mutation…
Graded quantum cluster algebras of infinite rank as colimits
Jan E. Grabowski, Sira Gratz
We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of i…
Cluster algebras of infinite rank as colimits
Sira Gratz
We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of roo…
Mutation of torsion pairs in cluster categories of Dynkin type
Sira Gratz
Mutation of torsion pairs in triangulated categories and its combinatorial interpretation for the cluster category of Dynkin type and of type have been studied by…
Cluster algebras of infinite rank
Jan E. Grabowski, Sira Gratz
Holm and Jorgensen have shown the existence of a cluster structure on a certain category that shares many properties with finite type cluster categories and that can be fru…