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arXiv · 2504.20931

Generalized cluster algebras are subquotients of cluster algebras

Rolando Ramos·David Whiting
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Abstract

Generalized Cluster Algebras (GCA) are generalizations of Cluster Algebras (CA) with higher-order exchange relations. Previously, Chekhov-Shapiro conjectured that every GCA can be embedded into a CA. In this paper, we prove a modified version of this conjecture by providing a construction that realizes a given GCA as subquotient of some CA, as an algebra over the ground ring of the GCA via restriction of scalars.

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Rolando Ramos, David Whiting. 2025-04-29. Generalized cluster algebras are subquotients of cluster algebras. https://arxiv.org/abs/2504.20931

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