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Comments on Exchange Graphs in Cluster Algebras

Title
Comments on Exchange Graphs in Cluster Algebras
Authors
Kim, Hyun KyuYamazaki, Masahito
Ewha Authors
김현규
Issue Date
2020
Journal Title
EXPERIMENTAL MATHEMATICS
ISSN
1058-6458JCR Link

1944-950XJCR Link
Citation
EXPERIMENTAL MATHEMATICS vol. 29, no. 1, pp. 79 - 100
Keywords
Cluster algebraexchange graphdilogarithm identity
Publisher
TAYLOR &

FRANCIS INC
Indexed
SCI; SCIE; SCOPUS WOS 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.
DOI
10.1080/10586458.2018.1437849
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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