Generalized cluster algebras are subquotients of cluster algebras
Rings and Algebras
2025-05-16 v3 Commutative Algebra
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.
Cite
@article{arxiv.2504.20931,
title = {Generalized cluster algebras are subquotients of cluster algebras},
author = {Rolando Ramos and David Whiting},
journal= {arXiv preprint arXiv:2504.20931},
year = {2025}
}
Comments
27 pages