51 citations · 264 across the 70 of their papers we have counts for
38 papers · 1 filter
Splitting torsion classes in higher homological algebra
Erlend D. Børve, Peter Jorgensen, Mads Hustad Sandøy
Let be an integer, a suitable -abelian category. There is a notion of higher torsion classes in , also known as -torsion classes. W…
A brief introduction to the -shaped derived category
Henrik Holm, Peter Jorgensen
A chain complex can be viewed as a representation of a certain quiver with relations, . The vertices are the integers, there is an arrow $q \xrightarrow{} q…
The -shaped derived category of a ring -- compact and perfect objects
Henrik Holm, Peter Jorgensen
In a previous work we constructed the -shaped derived category of any ring for any suitably nice category . The -shaped derived category of , which is denoted by $\…
The index with respect to a rigid subcategory of a triangulated category
Peter Jørgensen, Amit Shah
Palu defined the index with respect to a cluster tilting object in a suitable triangulated category, in order to better understand the Caldero-Chapoton map that exhibits the connec…
Proper abelian subcategories of triangulated categories and their tilting theory
Peter Jorgensen
In the theory of triangulated categories, we propose to replace hearts of -structures by proper abelian subcategories, which may be plentiful even when hearts are not. For insta…
Grothendieck groups of -exangulated categories and a modified Caldero-Chapoton map
Peter Jørgensen, Amit Shah
A strong connection between cluster algebras and representation theory was established by the cluster category. Cluster characters, like the original Caldero-Chapoton (CC) map, are…
Abelian subcategories of triangulated categories induced by simple minded systems
Peter Jorgensen
If is a field, a finite dimensional -algebra, then the simple -modules form a simple minded collection in the derived category $\operatorname{D}^b( \operatorname{mod}…
Classification of higher wide subcategories for higher Auslander algebras of type A
Martin Herschend, Peter Jorgensen
A subcategory of an abelian category is called wide if it is closed under kernels, cokernels, and extensions. Wide subcategories are of interest in representation the…
Green groupoids of 2-Calabi--Yau categories, derived Picard actions, and hyperplane arrangements
Peter Jorgensen, Milen Yakimov
We present a construction of (faithful) group actions via derived equivalences in the general categorical setting of algebraic 2-Calabi--Yau triangulated categories. To each algebr…
Model categories of quiver representations
Henrik Holm, Peter Jorgensen
Gillespie's Theorem gives a systematic way to construct model category structures on , the category of chain complexes over an abelian category $\mathsc…
Maximal -rigid pairs
Karin M. Jacobsen, Peter Jorgensen
Let be a -Calabi--Yau triangulated category, a cluster tilting object with endomorphism algebra . Consider the functor $\mathscr T( T,- ) : \mathscr T \right…
Tropical friezes and the index in higher homological algebra
Peter Jorgensen
Cluster categories and cluster algebras encode two dimensional structures. For instance, the Auslander--Reiten quiver of a cluster category can be drawn on a surface, and there is…
-abelian quotients of -angulated categories
Karin M. Jacobsen, Peter Jorgensen
Let be a triangulated category. If is a cluster tilting object and is the ideal of morphisms factoring through an object of $\oper…
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 .
Wide subcategories of -cluster tilting subcategories
Martin Herschend, Peter Jorgensen, Laertis Vaso
A subcategory of an abelian category is wide if it is closed under sums, summands, kernels, cokernels, and extensions. Wide subcategories provide a significant interface between re…
Co-t-structures: The First Decade
Peter Jorgensen
Co-t-structures were introduced about ten years ago as a type of mirror image of t-structures. Like t-structures, they permit to divide an object in a triangulated category T into…
Torsion classes and t-structures in higher homological algebra
Peter Jorgensen
Higher homological algebra was introduced by Iyama. It is also known as -homological algebra where is a fixed integer, and it deals with -cluster tilting subcatego…
Generalised friezes and a modified Caldero-Chapoton map depending on a rigid object, II
Thorsten Holm, Peter Jorgensen
It is an important aspect of cluster theory that cluster categories are "categorifications" of cluster algebras. This is expressed formally by the (original) Caldero-Chapoton map X…
Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes
Osamu Iyama, Peter Jorgensen, Dong Yang
If (A,B) and (A',B') are co-t-structures of a triangulated category, then (A',B') is called intermediate if A \subseteq A' \subseteq ΣA. Our main results show that intermediate co-…
Generalised friezes and a modified Caldero-Chapoton map depending on a rigid object
Thorsten Holm, Peter Jorgensen
The (usual) Caldero-Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps "reachabl…
Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D
Thorsten Holm, Peter Jorgensen, Martin Rubey
We give a complete classification of torsion pairs in the cluster category of Dynkin type D_n, via a bijection to new combinatorial objects called Ptolemy diagrams of type D. For t…
Torsion pairs in cluster tubes
Thorsten Holm, Peter Jorgensen, Martin Rubey
We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptol…
Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
Thorsten Holm, Peter Jorgensen
This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category C with the following properties. On the one hand…
Triangulated subcategories of extensions, stable t-structures, and triangles of recollements
Peter Jorgensen, Kiriko Kato
In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated an…