Every finitely generated abelian group is the class group of a generalized cluster algebra
Commutative Algebra
2025-05-01 v2
Abstract
We determine the class group of those generalized cluster algebras that are Krull domains. In particular, this provides a criterion for determining whether or not a generalized cluster algebra is a UFD. In fact, any finitely generated abelian group can be realized as the class group of a generalized cluster algebra. Additionally, we show that generalized cluster algebras are FF-domains and that their cluster variables are strong atoms. Finally, we examine the factorization and ring-theoretic properties of Laurent phenomenon algebras.
Cite
@article{arxiv.2411.14963,
title = {Every finitely generated abelian group is the class group of a generalized cluster algebra},
author = {Mara Pompili},
journal= {arXiv preprint arXiv:2411.14963},
year = {2025}
}