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

2025/04/11 by Oya, Hironori · 4 citations
#13F60 #17B10 #20G07 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2504.09011

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 F₄.

Cited by

• Reductive monoids and cluster algebras
• Integral cluster structures on quantized coordinate rings
• An introduction to (G,c)-bands
• An introduction to representation-theoretic canonical bases of cluster algebras

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