DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal Pub Date : 2023-12-21 DOI:10.1017/nmj.2023.15

TOMOKI NAKANISHI

引用次数: 0

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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群集散射图中的稀对数等式

我们将簇代数中 y 变量（系数）的概念扩展到簇散射图（CSD）。相应地，我们将与簇模式中的周期相关的稀对数特性扩展为与 CSD 中的环相关的稀对数特性。我们证明，通过应用可能无限次的五边形特征，这些特征可以构造并简化为微不足道的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.