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Cluster algebras and snake modules

Web20.I. Assem, R. Schi er and K. Serhiyenko, Modules over cluster-tilted algebras that do not lie on local slices, Archiv Math. 110, (2024) 9{18. ... C˘anak˘c and R. Schi er, Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings,_ Int. Math. Res. Not. rnx157 (2024) 1-82. WebIn 2010, Hernandez and Leclerc studied connections between representations of quantum affine algebras and cluster algebras. In 2024, Brito and Chari defined a family of …

Hernandez-Leclerc modules and snake graphs - NASA/ADS

Web3 Snake graphs and expansion formulas 23 ... Cluster algebras were introduced by Fomin and Zelevinsky [FZ1] in 2002. Their original motivation was coming from canonical bases in Lie Theory. Today cluster algebras are connected to various elds of mathematics, in-cluding Combinatorics (polyhedra, frieze patterns, green sequences, snake graphs, WebAug 14, 2015 · Cluster algebras and snake modules @article{Duan2015ClusterAA, title={Cluster algebras and snake modules}, author={Bing Duan and Jian-Rong Li and Yanfeng Luo}, journal={Journal of Algebra}, year={2015} } B. Duan, Jian-Rong Li, Yanfeng Luo; Published 14 August 2015; Mathematics; Journal of Algebra cfc filing https://ssbcentre.com

[1508.03467v3] Cluster algebras and snake modules

WebMay 1, 2024 · This paper establishes a connection between binary subwords and perfect matchings of a snake graph, an important tool in the theory of cluster algebras. Every binary expansion w can be associated to a piecewise-linear poset P and a snake graph G. We construct a tree structure called the antichain trie which is isomorphic to the trie of … WebSep 20, 2024 · Abstract. In 2010, Hernandez and Leclerc studied connections between representations of quantum affine algebras and cluster algebras. In 2024, Brito and … WebJul 5, 2024 · Recently, Duan and Schiffler in [16] proved the geometric q-character formula for snake modules of types A n and B n , and characterized the general kernel … cfc filters

Snake Graph Calculus and Cluster Algebras from Surfaces III: …

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Cluster algebras and snake modules

Cluster algebras and continued fractions Ilke C˘anak˘c

WebJun 10, 2013 · CLUSTER ALGEBRAS: AN INTRODUCTION 3 2. What is a cluster algebra? In this section we will define the notion of cluster algebra, first introduced by Fomin and Zelevinsky in [13]. For the purpose of acquainting the reader with the basic notions, in Section2.1 we will give the simple but somewhat restrictive WebRepresentations of quantum affine algebras Snake modules The simple module L(Y i T;aqkT:::Y i 2;aqk2 Y i 1;aqk1) is called a snake module/prime snake module/minimal …

Cluster algebras and snake modules

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WebMay 13, 2024 · As an application, we show that snake modules correspond to cluster monomials with square free denominators and we show that snake modules are real modules. We also show that the...

WebKeywords: cluster algebras, continued fractions, snake graphs. The rst author was supported by EPSRC grant number EP/N005457/1 and by Durham University, and the ... Corollary6.11for a rst result), string modules and string objects in the module categories and cluster categories of triangulated marked surfaces [BZ11,QZ17,Lab16], … WebMar 30, 2024 · The developed techniques allow defining snake graphs, which after suitable procedures, build Kronecker modules. We compute the dimension of the Brauer …

WebSep 1, 2024 · The notion of cluster algebras was introduced by Fomin and Zelevinsky [15] as a tool for studying canonical bases of quantum groups and total positivity for … WebMay 22, 2024 · As an application, we show that snake modules correspond to cluster monomials with square-free denominators and we show that snake modules are real …

WebApr 19, 2024 · The first section is a short introduction to cluster algebras, and Sects. 2, 3, and 4 are devoted to cluster algebras from surfaces, especially to the expansion formulas for the cluster variables and the construction of …

WebMay 29, 2015 · Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula whose … cfc fightingWebMay 13, 2024 · Moreover, we give a combinatorial formula for the -polynomial of the generic kernel associated to the snake module. As an application, we show that snake modules correspond to cluster monomials with square free denominators and we show that snake modules are real modules. bwp production videosWebMay 13, 2024 · As an application, we show that snake modules correspond to cluster monomials with square free denominators and we show that snake modules are real … bw pr col l\u0027horsetoWeb1.2. Hernandez-Leclerc modules, snake graphs, and q-characters 3 1.3. A recursive formula for Hernandez-Leclerc modules 5 2. Preliminary 5 2.1. Cluster algebras 5 2.2. … bwp releaseWebMay 22, 2024 · In 2010, Hernandez and Leclerc studied connections between representations of quantum affine algebras and cluster algebras. In 2024, Brito and … cfcf inmateWebSep 1, 2024 · The notion of cluster algebras was introduced by Fomin and Zelevinsky [15] ... [28] gave an explicit path description of q-characters for snake modules of types A n and B n. Brito and Mukhin [3] extended Mukhin-Young's methods to q-characters of extended-snake modules of type B n. cfcf inmate chargesWebSep 20, 2024 · Download a PDF of the paper titled Hernandez-Leclerc modules and snake graphs, by Bing Duan and 1 other authors Download PDF Abstract: In 2010, Hernandez … bwp race cheval