21 citations · 89 across the 14 of their papers we have counts for
13 papers · 1 filter
Cluster structures via representation theory: cluster ensembles, tropical duality, cluster characters and quantisation
Jan E. Grabowski, Matthew Pressland
We develop a general theory of cluster categories, applying to a 2-Calabi-Yau extriangulated category and cluster-tilting subcategory satisfying only mi…
Cluster categories for completed infinity-gons I: Categorifying triangulations
İlke Çanakçı, Martin Kalck, Matthew Pressland
Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity-gons, which are discs with an infinite closed set of marked points on their boundary…
Reduction of Frobenius extriangulated categories
Eleonore Faber, Bethany Rose Marsh, Matthew Pressland
We describe a reduction technique for stably 2-Calabi--Yau Frobenius extriangulated categories with respect to a functorially finite rigid subcategory .…
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
Xin Fang, Mikhail Gorsky, Yann Palu +2
We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpre…
Perfect matching modules, dimer partition functions and cluster characters
İlke Çanakçı, Alastair King, Matthew Pressland
Cluster algebra structures for Grassmannians and their (open) positroid strata are controlled by a Postnikov diagram D or, equivalently, a dimer model on the disc, as encoded by ei…
From frieze patterns to cluster categories
Matthew Pressland
Motivated by Conway and Coxeter's combinatorial results concerning frieze patterns, we sketch an introduction to the theory of cluster algebras and cluster categories for acyclic q…
Calabi-Yau properties of Postnikov diagrams
Matthew Pressland
We show that the dimer algebra of a connected Postnikov diagram in the disc is bimodule internally 3-Calabi-Yau in the sense of the author's earlier work. As a consequence, we obta…
Mutation of frozen Jacobian algebras
Matthew Pressland
We survey results on mutations of Jacobian algebras, while simultaneously extending them to the more general setup of frozen Jacobian algebras, which arise naturally from dimer mod…
Special tilting modules for algebras with positive dominant dimension
Matthew Pressland, Julia Sauter
We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-i…
A categorification of acyclic principal coefficient cluster algebras
Matthew Pressland
In earlier work, the author introduced a method for constructing a Frobenius categorification of a cluster algebra with frozen variables by starting from the data of an internally…
Graded Frobenius cluster categories
Jan E. Grabowski, Matthew Pressland
Recently the first author studied multi-gradings for generalised cluster categories, these being 2-Calabi-Yau triangulated categories with a choice of cluster-tilting object. The g…
Internally Calabi-Yau algebras and cluster-tilting objects
Matthew Pressland
We describe what it means for an algebra to be internally d-Calabi-Yau with respect to an idempotent. This definition abstracts properties of endomorphism algebras of (d-1)-cluster…
Labelled seeds and the mutation group
Alastair King, Matthew Pressland
We study the set S of labelled seeds of a cluster algebra of rank n inside a field F as a homogeneous space for the group M_n of (globally defined) mutations and relabellings. Regu…