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This work aims to establish a relationship between the coordinate rings of simply-connected simple algebraic groups and cluster algebras.

March 7, 2026Proceedings of the American Mathematical Society

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

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This work aims to establish a relationship between the coordinate rings of simply-connected simple algebraic groups and cluster algebras.
Analyzed the coordinate ring of a simply-connected simple algebraic group G
Compared it to the Berenstein–Fomin–Zelevinsky cluster algebra
Focused on cases where G is not of type F4
The coordinate ring coincides with the cluster algebra under specified conditions
Provides insights into the structure of algebraic groups and their relations to cluster algebras

Implication

This note demonstrates the correspondence of coordinate rings and cluster algebras in specific algebraic groups, suggesting new mathematical insights.

Abstract

We show that the coordinate ring of a simply-connected simple algebraic group G G over the complex number field coincides with the Berenstein–Fomin–Zelevinsky cluster algebra and its upper cluster algebra, at least when G G is not of type F 4 F_4 .

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Hironori Oya (2026) studied this question.

synapsesocial.com/papers/69abc1645af8044f7a4e9faa https://doi.org/10.1090/proc/17551

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Implication

This note demonstrates the correspondence of coordinate rings and cluster algebras in specific algebraic groups, suggesting new mathematical insights.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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