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DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  21 December 2023

TOMOKI NAKANISHI Open the ORCID record for TOMOKI NAKANISHI [Opens in a new window]
TOMOKI NAKANISHI*
Affiliation:
Graduate School of Mathematics Nagoya University Furo-cho, Chikusa-ku Nagoya Japan
*
nakanisi@math.nagoya-u.ac.jp
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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.

MSC classification

Primary: 13F60: Cluster algebras

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Type
Article
Information
Nagoya Mathematical Journal , Volume 253 , March 2024 , pp. 1 - 22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

This work is supported in part by the Japan Society for the Promotion of Science Grant No. JP16H03922.

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