The cluster category of a canonical algebra

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August undefined, 2024

WebDefinition: Canonical algebra. Basic terms for canonical algebras: The tubes, their rank, left rank, right rank, the mouth, the wings Separating property. Separating substructures Note: By definition, the piecewise hereditaryalgebras are those finite dimensional algebras B such that Db(mod B) is equivalent to Db(H) for some WebSep 1, 2024 · We say that a 2-Calabi–Yau tilted algebra End C T is of canonical type if the 2-Calabi–Yau category C is the cluster category of a canonical algebra. The proof of the next theorem follows closely the proof of Theorem 3.4 in [4]. Theorem 3.1. Let C …

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WebWe study the cluster category of a canonical algebra in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line . As an application we … WebLet k be a field and A a finite-dimensional k-algebra of global dimension ≤ 2. We construct a triangulated category CA associated to A which, if A is hereditary, is triangle equivalent to the cluster category of A. When CA is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. chris hein strings compact free download

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WebJan 29, 2008 · The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra … WebJSTOR Home chris heiple obituary

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WebSep 7, 2011 · Cluster algebras were invented by S. Fomin and A. Zelevinsky [50] in the spring of the year 2000 in a project whose aim it was to develop a combinatorial approach to the … WebA cluster category is obtained by forming an appropriate quotient of the derived category of representations of a quiver. In this survey article, we describe the connections between … chris hein solo violin rutrackerWebKeywords. preprojective algebra, cluster algebra, °ag variety, rigid module, mutation, Frobenius category, semicanonical basis 1. Introduction Cluster algebras were invented by Fomin and Zelevinsky in 2001 [10]. One of the main motivations for introducing this new class of commutative algebras was to chris hein winds complete

"http://export.arxiv.org/abs/0801.4540 " - The cluster category of a canonical algebra

The cluster category of a canonical algebra

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WebWe study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. Web14 hours ago · A cluster algebra is a commutative algebra with a distinguished family of generators, called cluster variables, displaying special combinatorial properties. To …

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WebSep 28, 2010 · The algebra possesses four bases, a Poincaré–Birkhoff–Witt basis, a canonical basis, and their duals. We prove recursions for dual canonical basis elements. The recursions imply that every cluster variable in is the specialization of the dual of an appropriate canonical basis element. WebA cluster algebra A of rank n is a subalgebra of an ambient ﬁeld F isomorphic to a ﬁeld of rational functions in n variables. Each cluster algebra comes equipped with a distinguished set of generators called cluster variables; this set is a union of overlapping algebraically independent n-subsets of F called clusters. The clusters are ...

WebA nite dimensional algebra is cluster-tilted of canonical type if it is isomorphic to the endomorphism algebra of a cluster-tilting object in the cluster category C X associated to a weighted projective line X, see Section 2.4 for de nitions. By results of Keller [23] and Amiot [1], the basic cluster-tilted algebras of canon- WebA cluster algebra is constructed from an initial seed as follows. If we repeatedly mutate the seed in all possible ways, we get a finite or infinite graph of seeds, where two seeds are …

WebAlmost 20 years ago, Fomin and Zelevinsky [9] invented cluster algebra in order to create a combinatorial framework for the study of canonical bases in quantum groups and the study of total positivity in algebraic groups. A cluster algebra is a commutative algebra with a Web14 hours ago · Almost 20 years ago, Fomin and Zelevinsky [] invented cluster algebra in order to create a combinatorial framework for the study of canonical bases in quantum groups and the study of total positivity in algebraic groups.A cluster algebra is a commutative algebra with a distinguished family of generators, called cluster variables, …

Webcluster algebras and studied their basic properties. Note, that in the classical limit (q = 1) they give rise to a Poisson structure on the cluster algebra as introduced and studied in [31], see [4, Rem. 4.6]. The main motivation for this work wasto start a general theory of canonical bases for cluster algebras. [4] ﬁnishes with some

WebDec 2, 2024 · We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the ... chris hein strings taranesazWebAug 1, 2010 · The cluster category of a canonical algebra Authors: M. Barot Dirk Kussin Technische Universität Berlin Helmut Lenzing Universität Paderborn Abstract We study … genuine marine led lightingWebk-category H. Assuming H connected, by Happel’s classiﬁcation theo-rem this happens if and only if A is derived equivalent to a hereditary or a canonical algebra, see [5, 6]. In the ﬁrst case, we can choose H = modA where A is hereditary and in the second H = cohX, the category of coherent sheaves over a weighted projective line X, see [3]. genuine malachite bead braceletComments: 20 pages, 11 figures. Notes of a mini-course given at the CIRM in Apri… genuine marble top coffee tablesWebMay 1, 2024 · The cluster category is triangle equivalent to a 2 -CY triangulated category arising from preprojective algebra. The paper is structured as follows. Section 2 provides the required background from cluster-tilting theory, quivers with potentials and generalized cluster categories. In Section 3, we recollect basic properties for . genuine mahogany lumber priceWebWe study the cluster category of a canonical algebra in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line . As an application we determine the automorphism group of t… chris heiny allstateWebOct 1, 2013 · We show that all tubular (simply laced) cluster algebras are of exponential growth by two different methods: first by studying the automorphism group of the … genuine marketing group.com