Cluster tilting theory

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August undefined, 2024

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 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 …

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WebOct 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) … 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 … export to html

Cluster-Tilting Theory - DocsLib

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 ... 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) … 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 … bubble tea fresh meadows

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CLUSTER-TILTING SUBCATEGORIES IN …

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 … WebJun 1, 2007 · Cluster-tilting theory. In J. de la Peña & R. Bautista (Eds.), Trends in representation theory of algebras and related topics, contemporary mathematics (Vol. 406, p. 1 ... Origin. Relevance. Future. An appendix to the Handbook of tilting theory, L. Angeleri-Hügel, D. Happel & H. Krause (Eds.). LMS Lecture Notes Series (Vol. 332). … export to hondurasWebdeﬁnition 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 … export to html figma

"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 ... " - Cluster tilting theory

Cluster tilting theory

WebDec 29, 2010 · Download a PDF of the paper titled Tilting theory and cluster algebras, by Idun Reiten. Download PDF Abstract: We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted … WebCluster-tilting theory. A. B. Buan, R. Marsh. Published 2008. Mathematics. Cluster algebras were introduced by Fomin and Zelevinsky in order to understand the dual …

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WebJan 14, 2008 · 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 1, 2006 · On the other hand, various ideas and constructions within cluster theory admit a far reaching generalization within representation theory, giving rise to cluster …

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 … WebSep 20, 2013 · This is a generalization of Gabriel's theorem by cluster tilting theory. We call the above roots cluster-roots and investigate their properties. Furthermore, we …

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 … WebThe Fomin-Zelevinsky mutation of quivers plays an important role in the theory of cluster algebras initiated in [FZ]. There is, motivated by this theory via [MRZ], a mutation of cluster-tilting objects in cluster categories, and more generally Hom- nite triangulated 2-Calabi-Yau (2-CY for short) categories over an algebraically closed eld K ...

WebIn mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and …

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; export to html powershellWebTilting 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 … export to html in rWebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories exporttolightburn.gmsWebJul 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 ... bubble tea from whereWebJun 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 … bubble tea funshopWebAslak 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] export to kml arcgisWebDec 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. ... export to malaysia