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arXiv · 2203.06928

Generalized quantum cluster algebras: the Laurent phenomenon and upper bounds

Liqian Bai·Xueqing Chen·Ming Ding·Fan Xu
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Abstract

Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We also show that upper bounds coincide with the corresponding generalized quantum upper cluster algebras under the "coprimality" condition.

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Liqian Bai, Xueqing Chen, Ming Ding, Fan Xu. 2022-03-14. Generalized quantum cluster algebras: the Laurent phenomenon and upper bounds. https://arxiv.org/abs/2203.06928

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