Cluster tilting theory
http://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf WebJun 4, 2024 · Our approach to Theorem 1.1 relies on a development in representation theory: the cluster-tilting theory. Let C be a 2-Calabi-Yau triangulated category. An object T ∈ C is rigid if Ext C 1 ( T, T) = 0. An object T ∈ C is a cluster-tilting object if T is rigid and for X ∈ C with Ext C 1 ( T, X) = 0, we have that X ∈ add T, where add T is ...
Cluster tilting theory
Did you know?
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 that the cluster-tilting graph associated with is always connected. As a consequence, we establish the connectedness of the tilting graph for the category of … WebA discrete cluster categoryof Dynkin type A is a triangulated category C(Z) associated to a discrete subset Z⊆S1 of the unit circle with n < ∞limit points. It demonstrates cluster combinatorics of Dynkin type A. In particular, it has cluster tilting subcategories, classified by Gratz, Holm and Jørgensen in [GHJ19], given
WebCLUSTER CATEGORIES OF TYPE A ∞ AND TRIANGULATIONS OF THE INFINITE STRIP. Shiping Liu, Charles Paquette. Published 2015. Mathematics. 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 …
WebJun 30, 2014 · In section 2 we have seen how the result that almost complete cluster-tilting objects in cluster categories have exactly two complements implied a similar result … WebJan 1, 2016 · An important property in cluster tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly 2 cluster-tilting objects ...
WebRelative cluster tilting objects in triangulated categories HTML articles powered by AMS MathViewer by Wuzhong Yang and Bin Zhu PDF Trans. Amer. Math. Soc. 371 ... Idun Reiten, and Gordana Todorov, Tilting theory and cluster combinatorics, Adv. Math. 204 (2006), no. 2, 572–618. MR 2249625, DOI 10.1016/j.aim.2005.06.003;
http://users.uoi.gr/abeligia/ natural foods to reduce high cholesterolWebJul 1, 2009 · For these 2-Calabi–Yau categories, we construct cluster-tilting objects associated with each reduced expression. The associated quiver is described in terms of the reduced expression. Motivated by the theory of cluster algebras, we formulate the notions of (weak) cluster structure and substructure, and give several illustrations of these ... natural food store farmington maineWebof the cluster algebras introduced in [FZ] by Fomin and Zelevinsky in the acyclic case. They also provide a generalized framework for classical tilting theory, with the cluster tilting … marial lodge incWebAug 1, 2024 · In Section 2, we recall basic definitions and facts for cluster-tilting theory. Section 3 is devoted to investigate the subfactors of cluster categories. In particular, Theorem 3.3 and Theorem 3.8 are proved. We then apply results obtained in Section 3 to prove Theorem 4.9 in Section 4. maria locke aboriginalWebCluster 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 … natural food store grand island neWebAug 20, 2006 · In this model, the tilting objects correspond to the clusters of Fomin–Zelevinsky. Using approximation theory, we investigate the tilting theory of C, … mariallull bellsouth.netWebtilting theory and cluster-tilting theory together with a motivation fromcluster algebras.Then we will give an introduction to τ-tilting theory which was recently developed. 1. Introduction Let Λ be a finite dimensional algebra over an algebraically closed field k, for example k is the field of complex numbers. We always maria lockwood arcadia