A note on a cluster structure of the coordinate ring of a simple algebraic group

Hironori Oya

doi:10.1090/proc/17551

paper

A note on a cluster structure of the coordinate ring of a simple algebraic group

arXiv:2504.09011 · doi:10.1090/proc/17551

Abstract

We show that the coordinate ring of a simply-connected simple algebraic group $G$ over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and its upper cluster algebra, at least when $G$ is not of type $F_{4}$ .

13 pages. v2: Minor corrections. v3: Minor corrections. Journal version

References in corpus (1)

$A = U$ for cluster algebras from moduli spaces of $G$ -local systems