A refined multiplication formula for cluster characters
Representation Theory
2023-01-11 v2 Combinatorics
Rings and Algebras
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.
Cite
@article{arxiv.2301.01059,
title = {A refined multiplication formula for cluster characters},
author = {Bernhard Keller and Pierre-Guy Plamondon and Fan Qin},
journal= {arXiv preprint arXiv:2301.01059},
year = {2023}
}
Comments
18 pages, v2 updated references