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no. 4
Explicit forms in lower degrees of rank 2 cluster scattering diagrams
Akagi, Ryota1
1 Nagoya University Chikusaku Hurocho Nagoya Japan
Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 1021-1067.

In this paper, we study wall elements of rank 2 cluster scattering diagrams based on dilogarithm elements. We derive two major results. First, we give a method to calculate wall elements in lower degrees. By this method, we may see the explicit forms of wall elements including the Badlands, which is the complement of $G$-fan. In this paper, we write one up to 7 degrees. Also, by using this method, we derive some walls independent of their degrees. Second, we find a certain admissible form of them. In the proof of these facts, we introduce a matrix action on a structure group, which we call a similarity transformation, and we argue the relation between this action and ordered products.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.432
Classification: 13F60
Keywords: cluster algebra, scattering diagram

Akagi, Ryota 1

1 Nagoya University Chikusaku Hurocho Nagoya Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Akagi, Ryota. Explicit forms in lower degrees of rank 2 cluster scattering diagrams. Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 1021-1067. doi : 10.5802/alco.432. https://alco.centre-mersenne.org/articles/10.5802/alco.432/

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