Cluster tilting theory
WebJul 30, 2024 · In this article, we find a one-to-one correspondence between support τ -tilting (resp. τ -rigid) subcategories of / and maximal relative rigid (resp. relative rigid) … WebCluster categories and cluster-tilting theory were introduced in order to understand cluster algebras. These objects were defined using representations of quivers: a quiver …
Cluster tilting theory
Did you know?
WebTilting theory and cluster algebras Reiten, Idun; Abstract. We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background … WebDec 1, 2024 · In recent years, cluster tilting theory has gained traction in the study of representation theory of finite dimensional algebras, and in algebraic Lie theory. On one hand it is a tool to study combinatorial phenomena arising in cluster theory, in the context of additive categorifications of cluster algebras. ...
WebNov 10, 2004 · Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds to a tilting object in the cluster category. The cluster tilted algebra is the algebra of … 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 …
WebMar 4, 2004 · The theory of simple minded systems can be viewed as “negative cluster tilting theory”. In particular, the result that \(\langle \mathscr {S}\rangle \) is an abelian subcategory is a negative ... WebJan 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 …
WebAslak Bakke Buan and Robert Marsh - Cluster-tilting theory [ MR 2258039] Christof Geiß - Introduction to moduli spaces associated to quivers (with an appendix by Lieven Le Bruyn and Markus Reineke) [ MR 2258040] Andrew Hubery - From triangulated categories to Lie algebras: a theorem of Peng and Xiao [ MR 2258041]
WebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories factory plastic shredderWebJul 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 ... factory playersWebA 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 factory player counthttp://users.uoi.gr/abeligia/ factory playWebCluster-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 … factory playhouse hitchinWebNov 12, 2024 · Let $\\C$ be a triangulated category with a cluster tilting subcategory $\\T$. We introduce the notion of $\\T[1]$-cluster tilting subcategories (also called ghost cluster tilting subcategories) of $\\C$, which are a generalization of cluster tilting subcategories. We first develop a basic theory on ghost cluster tilting subcategories. Secondly, we … factory play portugalWebJan 7, 2024 · 5-7 January 2024, online. Programme. Recordings. Geometric and homological methods have long been two key approaches in representation theory. Geometric models have been developed in a wide variety of settings and underpin links between representation theory, cluster theory, combinatorics and symplectic geometry. does wabtec pay a dividend