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arXiv · 2504.09011

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

Hironori Oya
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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 $F_4$.

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Hironori Oya. 2025-04-11. A note on a cluster structure of the coordinate ring of a simple algebraic group. https://doi.org/10.1090/proc%2F17551

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