Cluster tilting theory
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 … WebAug 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, …
Cluster tilting theory
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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 … 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. ...
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 … 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 …
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 … 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;
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://users.uoi.gr/abeligia/ manual photography pdfWebHowever, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. The aim of this paper is to introduce $\tau $ -tilting theory, which … kphl msfs downloadWebJan 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 ... manual phoropterkphl x plane 11 sceneryWebThese 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. manual pioneer 309WebNov 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 … manual photo stitching softwareWebCluster-tilting theory. A. B. Buan, R. Marsh. Published 2008. Mathematics. Cluster algebras were introduced by Fomin and Zelevinsky in order to understand the dual … manual physical therapy winchester va