Generalized cluster algebras are subquotients of cluster algebras

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.