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arXiv · 2411.14963

Every finitely generated abelian group is the class group of a generalized cluster algebra

Mara Pompili
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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.

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Mara Pompili. 2024-11-22. Every finitely generated abelian group is the class group of a generalized cluster algebra. https://arxiv.org/abs/2411.14963

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