The cluster category of a canonical algebra

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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 … 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, …

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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 ... WebKeywords. 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 scrum based development

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WebCluster Categories Cluster Tilting Tilting Objects Let d > 1 be a positive integer. In this note, we consider the d-cluster-tilted algebras, i.e., algebras which appear as endomorphism … WebJan 29, 2008 · Abstract: We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective … 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. scrumbles chicken

Quantum Cluster Algebra of Kronecker Type and the Dual Canonical …

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WebCluster Category . Cluster Type . Tree Type. AbstractIn this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of typeÃ.We are particularly interested in their derived equivalence classification. 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- pc playlistWebquiver Qis of full rank, we show that the image of the algebra homomorphisms is in the corresponding quantum cluster algebra. 1. Background The Ringel-Hall algebra H(A) of a (small) ﬁnitary abelian category A was in-troduced by Ringel ([13]). When A is the category RepF q Q of ﬁnite dimensional scrumbles business

"Comments: 20 pages, 11 figures. Notes of a mini-course given at the CIRM in Apri… " - The cluster category of a canonical algebra

The cluster category of a canonical algebra

[0801.4540v1] The cluster category of a canonical …

WebSep 28, 2011 · We apply our previous work on cluster characters for Hom-infinite cluster categories to the theory of cluster algebras. We give a new proof of Conjectures 5.4, 6.13, 7.2, 7.10 and 7.12 of Fomin and Zelevinsky’s Cluster algebras IV [Compositio Math. 143 (2007), 112–164] for skew-symmetric cluster algebras. We also construct an explicit … WebOct 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 corresponding cluster category and second by giving explicit sequences of mutations. References (26) B. Keller et al. Derived equivalences from mutations of quivers with …

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WebAug 1, 2010 · The cluster category of a canonical algebra Authors: M. Barot Dirk Kussin Technische Universität Berlin Helmut Lenzing Universität Paderborn Abstract We study … 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 $\mathbb {X}$. As …

WebJun 3, 2024 · , The cluster category of a canonical algebra, Trans. Amer. Math. Soc. 362 (8) (2010), 4313 – 4330. 10.1090/S0002-9947-10-04998-6 Google Scholar [4] Baur , K. and Bogdanic , D. , Extensions between Cohen–Macaulay modules of Grassmannian cluster categories , J. Algebraic Combin. 4 ( 2016 ), 1 – 36 . 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 results obtained by G. Lusztig concerning total positivity in algebraic groups [103] on the one hand and canonical bases in quantum groups [102] on the other hand (let us stress …

Web(i) A is canonical with weight sequence (p1;:::;pt) having at least one even weight. (ii) A is tubular, (iii) A is hereditary of nite representation type. The remaining canonical cases are covered by the next result. Theorem 1.3. Assume C = C(A) is the cluster category of a canonical algebra A with weight sequence (p1;:::;pt), where all weights ... WebJan 19, 2011 · Abstract Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the...

WebarXiv:0807.1960v11 [math.RT] 19 Mar 2010 CLUSTER ALGEBRAS, QUIVER REPRESENTATIONS AND TRIANGULATED CATEGORIES BERNHARD KELLER Abstract. This is an introduction to some aspects of

Web14 hours ago · A cluster algebra is a commutative algebra with a distinguished family of generators, called cluster variables, displaying special combinatorial properties. To … scrumbles calmingWebOct 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 … scrum bingoWebOct 19, 2014 · Abstract. We show that the endomorphism ring of each cluster tilting object in a tubular cluster category is a finite dimensional Jacobian algebra which is tame of polynomial growth. Moreover, these Jacobian algebras are given by a quiver with a non-degenerate potential and mutation of cluster tilting objects is compatible with mutation of … scrumbler refused to connectWebSep 1, 2024 · With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be … scrumbles cakeWebA 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 … scrumbles cat treatshttp://export.arxiv.org/abs/0801.4540 scrumbles chicken cat foodWebDe nition 1 (a)A cluster algebra is of nite type if the number of clus-ters is nite. (b)A cluster algebra is of nite mutation type if the number of quivers that appear in the seeds is nite. … scrum best practices ppt