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Cluster tilting

WebApr 8, 2016 · DOI: 10.2140/pjm.2024.289.449 Corpus ID: 119309242; Cluster tilting modules and noncommutative projective schemes @article{Ueyama2016ClusterTM, title={Cluster tilting modules and noncommutative projective schemes}, author={Kenta Ueyama}, journal={arXiv: Rings and Algebras}, year={2016} } WebJul 19, 2024 · We study a condition when the functor is dense and full, in another word, the ideal quotient becomes abelian. Moreover, a new equivalent characterization of cluster …

Tilting and cluster tilting for quotient singularities

WebCluster tilting theory is one of the most active areas in recent representation theory which is closely related to the notion of Fomin–Zelevinsky cluster algebras. It has an aspect of higher dimensional analogue of Auslander–Reiten theory, which is based on the notion of higher almost split sequences and higher Auslander algebras. ... WebJan 15, 2011 · The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n … trevor on yellowstone https://mobecorporation.com

CLUSTER-TILTING SUBCATEGORIES IN EXTRIANGULATED CATEG…

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 … WebJan 3, 2024 · 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-tilting objects in certain stably \((d-1)\)-Calabi–Yau Frobenius categories, as observed by Keller–Reiten.We show that an internally d-Calabi–Yau algebra … WebJan 1, 2016 · Moreover, for a 2-Calabi-Yau triangulated category C, it was showed in [1] that there is a close relation between cluster-tilting objects in C and support τ -tilting Λ-modules, where Λ is a 2 ... trevor osborne charitable trust

Tilting, cluster-tilting and -tilting - A brief introduction

Category:Introduction to Ï -tilting theory

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Cluster tilting

-cluster tilting subcategories for Nakayama algebras

WebMay 2, 2024 · We give a characterization of -cluster tilting subcategories of representation-directed algebras based on the -Auslander-Reiten translations. As an application we … WebCluster-tilted algebras and generalized APR-tilting As mentioned in Section 2, the main idea of (hereditary) tilting theory is to compare the representation theory of a hereditary algebra H with the representation theory of a tilted algebra Λ, obtained as the endomorphism ring of a tilting module T in mod H. op This motivates the investigation ...

Cluster tilting

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WebApr 1, 2008 · We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite-dimensional symmetric and satisfy τ 2 = id. In particular, we compute 2-CY tilted algebras ... WebFeb 15, 2024 · Let R be a cluster tilting object of T. Then an object T ∈ T is maximal R [1]-rigid with respect to T if and only if T is R [1]-cluster tilting. Combining Lemma 2.7 with Theorem 2.5, we obtain the following result which generalizes the work of Yang–Zhu [18, Theorem 1.2]. Corollary 2.8. Let R be a cluster tilting object of T with ...

WebJan 3, 2024 · A subcategory \({\mathcal {C}}\) of \({\mathcal {B}}\) is cluster tilting if \({\mathcal {C}}\) is a pre-cluster tilting and \({\mathcal {C}}={\mathcal {C}}^{\bot … WebCluster-tilting theory gives a way to construct abelian categories from some triangu- lated categories and exact categories. Let Tbe a cluster-tilting subcategory in a cluster …

WebApr 23, 2008 · Abstract. We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This … WebSep 17, 2024 · Furthermore, mutation of cluster tilting objects is consistent with mutation of seed data, i.e. the pair associated to the mutated object μ k (T) is the mutated pair μ k (B, L). This theorem means that our original category CM (A) provides consistent quasi-commutation rules for quantum clusters, by direct computation from cluster tilting ...

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WebCluster-tilting theory Aslak Bakke Buan and Robert Marsh Abstract. Cluster algebras were introduced by Fomin and Zelevinsky in or- der to understand the dual canonical basis of … tenerife spain weather in novemberWebCluster-tilting theory A. B. Buan, R. Marsh Published 2008 Mathematics Cluster algebras were introduced by Fomin and Zelevinsky in order to understand the dual canonical … tenerife speckled lizardWebJun 5, 2024 · We also deduce that the Gorenstein projectives of { {\mathcal {E}}} admit a d\mathbb {Z} -cluster tilting subcategory under some assumptions. Finally, we compute the d\mathbb {Z} -cluster tilting subcategory of the singularity category for a finite-dimensional algebra which is not Iwanaga–Gorenstein. trevor ormes hamiltonWebApr 8, 2024 · The James Webb Space Telescope captured 50,000 sources of near-infrared light in a new image of Pandora's Cluster, a megacluster of galaxies. ... The planet is unique in its tilt to its side ... trevor ottleyWebMoreover, 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 ... trevor ornamental designs nottingham reviewWebJun 11, 2024 · In this paper, we show that under suitable circumstances, the Grothendieck group of ${\mathcal{C}}$, denoted by $K_{0}({\mathcal{C}})$, can be expressed as a … tenerife special offersWebDec 29, 2010 · In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our method is based on higher dimensional Auslander … trevor osborne property group