2024 Cluster tilting theory

Cluster tilting theory

Author: zxnv

August undefined, 2024

Webdeﬁnition of cluster categories; we also give an introduction to cluster-tilting theory and describe a graphical method for deﬁning cluster categories in type A; in Section 4 we describe cluster-tilted algebras with particular emphasis on the case of ﬁnite … 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 …

[math/0402054] Tilting theory and cluster combinatorics

Webtilting 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 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 ... crewsaver crewfit+ 180n pro lifejacket

[1012.6014] Tilting theory and cluster algebras - arXiv.org

WebIn mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and … WebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories crewsaver crewfit junior

Tilting and cluster tilting for quotient singularities SpringerLink

Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated ...

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 ... WebJan 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. buddy bi rightWebCluster 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 … crewsaver crew holdall

"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

Cluster tilting theory

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] WebJul 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 ...

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Webcluster-tilting objects, which generalize tilting modules. In this case there are 14 cluster-tilting objects where the symbol ⊕ is omitted and the edges indicate mutation. … 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 …

WebMar 26, 2024 · Based on tilting theory and cluster tilting theory, we construct some commutative Cohen-Macaulay rings of hereditary representation type. First we give a general existence theorem of cluster tilting module or non-commutative crepant resolutions on the Segre product of two commutative Gorenstein rings whenever each factor has … WebSep 1, 2008 · Cluster categories and cluster-tilting theory were introduced in order to understand cluster algebras. These objects were defined using representations of …

WebCluster theory is a theory of strategy.. Alfred Marshall, in his book Principles of Economics, published in 1890, first characterized clusters as a "concentration of specialized … 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 …

WebJan 22, 2024 · The constructions of “mutations” are known before in different contexts, including cluster tilting theory, silting theory, τ-tilting theory, cluster algebras and …

WebThese grew from categorical models for cluster algebras. In particular, the cluster-tilted algebras arising from cluster categories have given new insights into classical tilting theory. The interaction is in both directions, with the representation-theoretic models also being used to answer fundamental questions about cluster algebras. buddy biographyWebOct 3, 2012 · 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. Reformulated for path algebras kQ, this says that an almost complete support tilting modules has exactly two complements. We generalize (support) … crewsaver crewfit 40 proWebCluster-tilting theory. A. B. Buan, R. Marsh. Published 2008. Mathematics. Cluster algebras were introduced by Fomin and Zelevinsky in order to understand the dual … crewsaver drysuit repairWebTilting 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 … crewsaver crewfit 275nWebJul 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) … crewsaver crewfit 275n life jacketshttp://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf crewsaver drysuit sizesWebA. Beligiannis: ''Relative Homology and Higher Cluster Tilting Theory'', pdf, Oberwolfach Reports, Volume 8, Issue 1, (2011), 534-537. Preprints in Preparation - Work in Progress A. Beligiannis: ''Relative Homology, Tilting Objects and Freyd's Generating Hypothesis ... buddy bi rite rent to own