A note on a cluster structure of the coordinate ring of a simple algebraic group
Representation Theory
2026-04-02 v3 Rings and Algebras
Abstract
We show that the coordinate ring of a simply-connected simple algebraic group over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and its upper cluster algebra, at least when is not of type .
Keywords
Cite
@article{arxiv.2504.09011,
title = {A note on a cluster structure of the coordinate ring of a simple algebraic group},
author = {Hironori Oya},
journal= {arXiv preprint arXiv:2504.09011},
year = {2026}
}
Comments
13 pages. v2: Minor corrections. v3: Minor corrections. Journal version