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arXiv · 2301.01059

A refined multiplication formula for cluster characters

Bernhard Keller·Pierre-Guy Plamondon·Fan Qin
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Abstract

We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. As an application, we show that for cluster algebras of acyclic types, specialization of a cluster variable to 1 sends all cluster variables to elements of a cluster algebra of smaller rank. We also obtain application to the reduction of friezes of acyclic type.

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Bernhard Keller, Pierre-Guy Plamondon, Fan Qin. 2023-01-03. A refined multiplication formula for cluster characters. https://arxiv.org/abs/2301.01059

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