33 citations · 188 across the 19 of their papers we have counts for
21 papers
Higher torsion classes, -tilting theory and silting complexes
Jenny August, Johanne Haugland, Karin M. Jacobsen +3
Initiated in work by Adachi, Iyama and Reiten, the area known as -tilting theory plays a fundamental role in contemporary representation theory. In this paper we explore a highe…
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…
Some applications of extriangulated categories
Yann Palu
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories and generalise both exact categories and triangulated categories. This survey article…
Hereditary extriangulated categories: Silting objects, mutation, negative extensions
Mikhail Gorsky, Hiroyuki Nakaoka, Yann Palu
In this article, we initiate the study of hereditary extriangulated categories. Many important categories arising in representation theory in connection with various theories of mu…
A generalization of perfectly clustering words and band bricks for certain gentle algebras
Benjamin Dequêne, Mélodie Lapointe, Yann Palu +3
We generalize the perfectly clustering words of Simpson and Puglisi and relate them to band bricks over certain gentle algebras. This allows us to prove a generalization of a conje…
A characterisation of higher torsion classes
Jenny August, Johanne Haugland, Karin M. Jacobsen +3
Let be an abelian length category containing a -cluster tilting subcategory . We prove that a subcategory of is a -torsion class if a…
Positive and negative extensions in extriangulated categories
Mikhail Gorsky, Hiroyuki Nakaoka, Yann Palu
We initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We show tha…
External triangulation of the homotopy category of exact quasi-category
Hiroyuki Nakaoka, Yann Palu
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a…
Associahedra for finite type cluster algebras and minimal relations between -vectors
Arnau Padrol, Yann Palu, Vincent Pilaud +1
We show that the mesh mutations are the minimal relations among the -vectors with respect to any initial seed in any finite type cluster algebra. We then use this a…
Non-kissing and non-crossing complexes for locally gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, or…
Auslander--Reiten theory in extriangulated categories
Osamu Iyama, Hiroyuki Nakaoka, Yann Palu
The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories. In this article, we develop Ausland…
Non-kissing complexes and tau-tilting for gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
We interpret the support -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously…
Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories
Hiroyuki Nakaoka, Yann Palu
We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categorie…
Algebras of finite representation type arising from maximal rigid objects
Aslak Bakke Buan, Yann Palu, Idun Reiten
We give a complete classification of all algebras appearing as endomorphism algebras of maximal rigid objects in standard 2-Calabi-Yau categories of finite type. Such categories ar…
From triangulated categories to module categories via homotopical algebra
Yann Palu
The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown…
Nearly Morita equivalences and rigid objects
Bethany Marsh, Yann Palu
If two cluster-tilting objects of an acyclic cluster category are related by a mutation, then their endomorphism algebras are nearly-Morita equivalent [Buan-Marsh-Reiten], i.e. the…
Coloured quivers for rigid objects and partial triangulations: The unpunctured case
Bethany Marsh, Yann Palu
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We sh…
A Caldero-Chapoton map for infinite clusters
Peter Jorgensen, Yann Palu
We construct a Caldero-Chapoton map on a triangulated category with a cluster tilting subcategory which may have infinitely many indecomposable objects. The map is not necessarily…
Cluster characters II: A multiplication formula
Yann Palu
Let be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on which are satisfied for…
Grothendieck Group and Generalized Mutation Rule for 2-Calabi--Yau Triangulated Categories
Yann Palu
We compute the Grothendieck group of certain 2-Calabi--Yau triangulated categories appearing naturally in the study of the link between quiver representations and Fomin--Zelevinsky…
Cluster characters for triangulated 2-Calabi--Yau categories
Yann Palu
Starting from an arbitrary cluster-tilting object in a 2-Calabi--Yau category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each ob…