@article{Bai2024, 
author = {Liqian Bai and Xueqing Chen and Ming Ding and Fan Xu},
title = {A generalized quantum cluster algebra of Kronecker type},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {1},
pages = {670-685},
keywords = {generalized quantum cluster algebra, cluster variable, cluster multiplication formula, positive basis, Kronecker quiver},
url = {https://www.sciopen.com/article/10.3934/era.2024032},
doi = {10.3934/era.2024032},
abstract = {The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra.}
}