This paper demonstrates that the infinitesimal dilogarithm satisfies cluster identities, highlighting its link to the pentagon relation.
In this paper, we show that the infinitesimal dilogarithm and Kontsevich's one-and-a-half logarithm function satisfies the identities which result from periods in cluster patterns. We also prove that these cluster identities are a consequence of the pentagon relation in the infinitesimal case.
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Sı̇nan Ünver (2025) studied this question.
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