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

Key Points

• 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