2024 Cluster tilting theory

Cluster tilting theory

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August undefined, 2024

WebCluster categories and cluster-tilting theory were introduced in order to understand cluster algebras. These objects were defined using representations of quivers: a quiver … 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 ...

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

WebSep 1, 2008 · Cluster categories and cluster-tilting theory were introduced in order to understand cluster algebras. These objects were defined using representations of … Webof 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 … the godfather movie download in tamil

On cluster-tilting graphs for hereditary categories - ScienceDirect

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 ... 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. ... 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. the godfather movie free on youtube

Triangulated categories with cluster-tilting subcategories

Cluster-Tilting Theory - DocsLib

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 … WebFeb 4, 2004 · Tilting theory and cluster combinatorics. We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived … theater auf tourWebMar 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 ... the godfather movie internet archive

"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 " - Cluster tilting theory

Cluster tilting theory

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) … http://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf

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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 … 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 …

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. 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 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 … 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]

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 …

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 … the godfather movie in hindi downloadWebJun 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). … theateraufführung romeo und juliaWebMar 14, 2024 · Positive Fuss–Catalan Numbers and Simple-Minded Systems in Negative Calabi–Yau Categories theaterauftaktWebRelative 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; the godfather movie giftsWebNov 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 … the godfather movie full movieWebThe 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 ... theater auflaufWebIntroduction Tilting Cluster-tilting ˝-tiltingBibliography BibliographyI O.Iyama,andI.Reiten,Introductionto˝-tiltingtheory,PNAS July8,2014111(27)9704-9711. the godfather movie memorabilia