Reductive monoids and cluster algebras
Representation Theory
2025-12-23 v2 Rings and Algebras
Abstract
We show that the coordinate ring of the Vinberg monoid of a simply connected semisimple complex group is an upper cluster algebra. As an application, we construct cluster structures on a large class of flat reductive monoids. After localization, we obtain cluster structures on any connected reductive group whose commutator group is simply connected.
Keywords
Cite
@article{arxiv.2512.09564,
title = {Reductive monoids and cluster algebras},
author = {Jinfeng Song and Jeff York Ye},
journal= {arXiv preprint arXiv:2512.09564},
year = {2025}
}
Comments
V2, 20 pages. We updated references