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자연과학대학
수학전공
Journal papers
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Comments on Exchange Graphs in Cluster Algebras
Title
Comments on Exchange Graphs in Cluster Algebras
Authors
Kim H.K.
;
Yamazaki M.
Ewha Authors
김현규
SCOPUS Author ID
김현규
Issue Date
2020
Journal Title
Experimental Mathematics
ISSN
1058-6458
Citation
Experimental Mathematics vol. 29, no. 1, pp. 79 - 100
Keywords
Cluster algebra
;
dilogarithm identity
;
exchange graph
Publisher
Taylor and Francis Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds. © 2018, © 2018 Taylor & Francis Group, LLC.
DOI
10.1080/10586458.2018.1437849
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