Relation between generalized and ordinary cluster algebras
Representation Theory
2026-01-13 v2 Commutative Algebra
Abstract
Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we show that the same property holds for any generalized cluster algebra with -variables in an arbitrary semifield. We also present the relations between the -matrices, the -matrices, and the -polynomials of a generalized cluster pattern and those of the corresponding composite cluster pattern.
Cite
@article{arxiv.2512.21062,
title = {Relation between generalized and ordinary cluster algebras},
author = {Ryota Akagi and Tomoki Nakanishi},
journal= {arXiv preprint arXiv:2512.21062},
year = {2026}
}
Comments
20 pages ver2: The claim on the Laurent positivity was removed