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arXiv · 2512.09564

Reductive monoids and cluster algebras

Jinfeng Song·Jeff York Ye
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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.

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Jinfeng Song, Jeff York Ye. 2025-12-10. Reductive monoids and cluster algebras. https://arxiv.org/abs/2512.09564

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