English

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 GG over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and its upper cluster algebra, at least when GG is not of type F4F_4.

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