2024 The cluster category of a canonical algebra

The cluster category of a canonical algebra

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WebDe 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. … 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

The cluster category of a canonical algebra - ar5iv.labs.arxiv.org

Comments: 20 pages, 11 figures. Notes of a mini-course given at the CIRM in Apri… 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 … common-bin

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Webk-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]. 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 … 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 … dtw to hilton head

Tubular cluster algebras II: Exponential growth

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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 … 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, … dtw to heathrow flight timeWebWe 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 … dtw to hillsdale mi

"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 ... " - The cluster category of a canonical algebra

The cluster category of a canonical algebra

Cluster algebras IV: Coefficients - Cambridge

http://export.arxiv.org/abs/0801.4540 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...

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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 … Webquiver 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

WebJSTOR Home 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.

WebJan 29, 2008 · Download PDF Abstract: We study the cluster category of a canonical algebra in terms of the hereditary category of coherent sheaves over the corresponding … WebMay 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 .

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.

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 common bill of sale formWebJul 15, 2011 · Abstract. We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular is associated to an elliptic root system. We show that via a cluster character the cluster ... common bills when rentingWebSep 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 … dtw to hilton head scWeb14 hours ago · A cluster algebra is a commutative algebra with a distinguished family of generators, called cluster variables, displaying special combinatorial properties. To … dtw to hnd flightsWebDec 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 ... dtw to hnl flight timeWebSep 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. dtw to hnlWebSep 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 … dtw to hkg flight