Let ℂq[SL(n + 1)] denote the quantum coordinate ring of the special linear group which has a quantum cluster structure denoted by \(\cal{A}_{q}\) . Let \(\cal{A}_{p,q}\) be the 2nd-stage quantization of the quantum cluster algebra \(\cal{A}_{q}\) , equipped with a compatible Poisson structure {–,–}. The purpose of this paper is to describe the structure of the 2nd-stage quantized cluster algebra \(\cal{A}_{p,q}\) . We prove that for n ⩾ 2, the 2nd-stage quantized cluster algebra \(\cal{A}_{p,q}\) is trivial. Additionally, we provide a detailed description of the compatible Poisson structure on \(\cal{A}_{q}\) .
