5 papers
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…
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.
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…