Quantum cluster algebras and their specializations
arXiv:1807.09826 · doi:10.1016/j.jalgebra.2019.04.033
Abstract
We show that in case a cluster algebra coincides with its upper cluster algebra and the cluster algebra admits a grading with finite dimensional homogeneous components, the corresponding Berenstein-Zelevinsky quantum cluster algebra can be viewed as a flat deformation of the classical cluster algebra.
11 pages, v2: small corrections and improvements after referee report. Final version, to appear in J. Algebra