Cluster tilting subcategories
WebJul 2, 2024 · We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra contains a -cluster tilting subcategory for some , then is a radical square zero Nakayama algebra. This gives a complete classification of weakly -representation finite gentle algebras ...
Cluster tilting subcategories
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WebFeb 26, 2024 · Cluster tilting objects in a triangulated category \(\mathcal {C}\) were introduced in [].When \(\mathcal {C}\) is a cluster category or more general, a 2-Calabi–Yau triangulated category, they have many nice properties from the perspective of mutations and play a crucial role in the categorification of cluster algebras (see [2, 7]).Adachi et al. [] … WebSep 1, 2024 · Let $ \mathscr{B} $ be an extriangulated category which admits a cluster tilting subcategory $ \mathcal{T} $. We firstly introduce notions of $ \mathcal{T} $-cluster tilting subcategories and ...
WebNov 12, 2024 · On cluster-tilting graphs for hereditary categories. Changjian Fu, Shengfei Geng. Let be a connected hereditary abelian category with tilting objects. It is proved … WebNov 12, 2024 · Wuzhong Yang, Panyue Zhou, Bin Zhu. Let $\C$ be a triangulated category with a cluster tilting subcategory $\T$ . We introduce the notion of $\T [1]$ -cluster …
WebMay 12, 2024 · Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% of your contribution will fund improvements and new initiatives to benefit arXiv's global scientific community. http://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf
WebAug 15, 2024 · The new notion that made Iyama's theory fundamental in representation theory, is the notion of n-cluster tilting subcategories [15, Definition 2.2], where n is a …
WebOn the monomorphism category of n-cluster tilting subcategories. Javad Asadollahi. Science China Mathematics. Let R be a commutative artinian ring. Let Λ be an artin R-algebra of finite representation type. Let Γ := End Λ (E) op be the Auslander algebra of Λ, where E is an additive generator of mod-Λ, the category of finitely presented Λ ... men\u0027s no tuck button down shirtsWebMay 2, 2024 · Laertis Vaso. We give a characterization of -cluster tilting subcategories of representation-directed algebras based on the -Auslander-Reiten translations. As an application we classify acyclic Nakayama algebras with homogeneous relations which admit an -cluster tilting subcategory. Finally, we classify Nakayama algebras of global … men\u0027s no tuck shirts short sleevesWebJan 15, 2011 · Abstract. The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n -Auslander–Reiten translation functor τ n plays an important role in the study of n -cluster tilting subcategories. We study the category M n of preinjective-like … how much to tip stateroom attendantWebAug 1, 2024 · Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2 ... men\u0027s no tuck golf shirtsWebIn particular, we shall show that the cluster-tilting subcategories are precisely given by compact tri- angulations. We first study the (canonical) orbit category of the bounded de- rived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on the case where the quiver is of infinite Dynkin ... men\u0027s no tuck short sleeve shirtsWebMay 2, 2024 · We also introduce mixed (pre)cluster tilting modules as a generalisation of (pre)cluster tilting modules, and establish an Auslander type correspondence by showing that dominant Auslander ... how much to tip ski instructorWebTRIANGULATED CATEGORIES WITH CLUSTER TILTING SUBCATEGORIES 705 then weak add.TT1U/-cluster tilting subcategories coincide with add.TT1U/-cluster tilting subcategories, and are also the same as TT1U-cluster tilting objects introduced in[Yang and Zhu 2024]. The first part of our work is to develop a basic theory of ghost cluster … how much to tip take out