The cluster category of a canonical algebra

Author: tqeu

August undefined, 2024

WebThe triple (x;y;Q) is called the initial seed of the cluster algebra A= A(x;y;Q). The cluster algebra is the ZP-subalgebra of Fgenerated by so-called cluster variables, and these cluster variables are constructed from the initial seed by a recursive method called mutation. A mutation transforms a seed (x;y;Q) into a new seed (x0;y0;Q0). Given ... WebJul 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 ...

Cluster-tilted and quasi-tilted algebras - ScienceDirect

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 … scoundrel\\u0027s tj

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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 … WebJun 21, 2016 · The cluster category of a canonical algebra. Trans. Amer. Math. Soc. 362 (8), 4313–4330 (2010) Article MathSciNet MATH Google Scholar Barot, M., Trepode, S.: Cluster tilted algebras with a cyclically oriented quiver. Comm. Algebra 41 (10), 3613–3628 (2013) Article MathSciNet MATH Google Scholar Comments: 20 pages, 11 figures. Notes of a mini-course given at the CIRM in Apri… scoundrel\\u0027s tb

[0801.4540] The cluster category of a canonical algebra - arXiv.org

Introduction C A k all k - UNAM

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 determine the automorphism group of t… WebJan 29, 2008 · The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra … scoundrel\\u0027s tlWebJan 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 … scoundrel\\u0027s to

"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 " - The cluster category of a canonical algebra

The cluster category of a canonical algebra

[0801.4540v1] The cluster category of a canonical …

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

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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. WebOct 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 …

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]. 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 …

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 … 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 .

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 …

WebSep 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 … scoundrel\\u0027s tnWeb14 hours ago · A cluster algebra is a commutative algebra with a distinguished family of generators, called cluster variables, displaying special combinatorial properties. To … scoundrel\\u0027s tmWebSep 16, 2024 · Later, S. Fomin and A. Zelevinsky studied the canonical bases for quantum groups and discovered the combinatorics of simple transformations and defined associated classical and quantum cluster algebras to such situations. In particular, Stasheff associahedra are associated to these cluster algebras. scoundrel\\u0027s smWeb(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 ... scoundrel\\u0027s tuWebJan 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... scoundrel\\u0027s trWebMay 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 . scoundrel\\u0027s tpWebarXiv: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 scoundrel\\u0027s t1