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 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 ... 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. ...
Tilting and Cluster Tilting for Preprojective Algebras and Coxeter ...
WebJun 11, 2024 · grothendieck groups of triangulated categories via cluster tilting subcategories - volume 244 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a … 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 ... mouth ulcer reason
Cluster tilting for higher Auslander algebras - ScienceDirect
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 … WebIntroduction Tilting Cluster-tilting ˝-tiltingBibliography BibliographyI O.Iyama,andI.Reiten,Introductionto˝-tiltingtheory,PNAS July8,2014111(27)9704-9711. 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 ... mouth ulcers and chemotherapy