Cluster tilting subcategories

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August undefined, 2024

WebMay 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 … WebMar 13, 2024 · • Cluster categories endowed with a ﬁxed cluster tilting object, and the maximal r ela- tive extriangulated structure making it pr ojective. In this case, the silting ob jects are

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WebDec 1, 2013 · Abstract. We prove that some subquotient categories of exact categories are abelian. This generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated … WebAug 10, 2024 · Abstract. We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact categories and triangulated categories. Let (\mathcal {C},\mathbb {E},\mathfrak {s}) be an extriangulated category with enough projectives \mathcal {P} and {\mathscr {M}} be a full … salem oregon fish store

Relative Rigid Subcategories and τ -Tilting Theory - Springer

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 ... Webthis we introduce cluster tilting subcategories of left triangulated categories, and we show that there is a correspondence between cluster tilting subcategories of Eand .Wealso … WebJul 19, 2024 · Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we … things to do on thursday island

[2010.13203] Higher Ideal Approximation Theory - arXiv.org

Quotients of exact categories by cluster tilting …

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 … WebIn 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 ... salem oregon food pantryWebAug 1, 2016 · Abelian Categories Arising from Cluster Tilting Subcategories. Yu Liu, Panyue Zhou; Mathematics. Appl. Categorical Struct. 2024; TLDR. The notion of pre-cluster tilting subcategory C is cluster tilting if and only if the factor category B / C is abelian, which is new for an exact category case. things to do on the south coast kzn

"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 … " - Cluster tilting subcategories

Cluster tilting subcategories

WebJun 13, 2024 · In this paper we introduce nZ-abelian and nZ-exact categories by axiomatising properties of nZ-cluster tilting subcategories. We study this categories and show that every nZ-cluster tilting … Expand. PDF. View 3 excerpts, cites background; Save. Alert. The role of gentle algebras in higher homological algebra. WebJun 8, 2024 · In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type A ∞ as introduced by Holm-Jørgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.

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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 … WebNov 20, 2024 · In particular, it has cluster tilting subcategories, classified by Gratz, Holm and Jørgensen in [GHJ19], given by suitable triangulations of the closed disc with marked points Z. While providing ...

WebOct 25, 2024 · On the other hand, ideal approximation theory, that is a gentle generalization of the classical approximation theory and deals with morphisms and ideals instead of objects and subcategories, is an active area that has been the subject of several researches. Our aim in this paper is to introduce the so-called `ideal approximation theory' into ... WebMoreover, 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-Calabi-Yau triangulated category ℬ , a functorially finite, extension closed subcategory 𝒯 of ℬ is cluster tilting if and only if ℬ /𝒯 is an ...

WebAug 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 ... 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 ...

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.

WebMay 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 ... things to do on valentine\u0027s day with friendsWebMoreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that … things to do on valentines day in gaWebMay 2, 2024 · Laertis Vaso. We give a characterization of -cluster tilting subcategories of representation-directed algebras based on the -Auslander-Reiten translations. As an … things to do on valentines with friendsWebCluster tilting subcategories are obviously strongly functorially finite maximal rigid subcategories, we prove that the converse is true if the 2-Calabi-Yau extriangulated categories admit a cluster tilting subcategories, which generalizes a result of Buan-Iyama-Reiten-Scott [BIRS] and Zhou-Zhu [ZZ]. ... things to do on tokyoWebJul 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 ... things to do on women\u0027s dayWebTRIANGULATED 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 … things to do on walpurgisnachthttp://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf things to do on the outskirts of philadelphia