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DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS
Published online by Cambridge University Press: 21 December 2023
Abstract
We extend the notion of y-variables (coefficients) in cluster algebras to cluster scattering diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a CSD. We show that these identities are constructed from and reduced to trivial ones by applying the pentagon identity possibly infinitely many times.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
Footnotes
This work is supported in part by the Japan Society for the Promotion of Science Grant No. JP16H03922.