x}, B,\Lambda)$ where $(B,\Lambda)$ where $B$ is as above and $\Lambda$ is a skew-symmetric $n\times n$-matrix such that $(B,\Lambda)$ is a [*compatible pair*]{} (see Section \[se:Cluster Algebras\] for details). The set ${\bf x}=(x_1,\ldots, x_n)$ now lives in the skew-field of fractions $\CC_\Lambda(x_1,\ldots,x_n)$ defined by $\Lambda$. A compatible pair also defines a compatible Poisson structure in the sense of [@GSV] on the cluster algebra given by $({\bf x},B)$. It is well-known that the conjectured quantum cluster algebra structures on the rings $R_q[G]$ and the standard Poisson structure on $\CC[G]$ arise from such a compatible pair. Therefore, we would like to suggest the following conjecture..

\[conj: homeo cluster\] Let $(B,\Lambda)$ be a compatible pair and let $\AA$ and $\AA_q$ be a cluster, resp. quantum cluster algebra defined by $({\bf x},B)$, resp. $({\bf x},B,\Lambda)$. Suppose further that $\AA$ and $\AA_q$ are Noetherian and that $\AA$ is the coordinate ring of the affine variety $X$. Then, there exists a homeomorphism between the space of primitive ideals of $\AA_q$ and the symplectic leaves on $X$ defined by $\Lambda$.

In light of Conjecture \[conj: homeo cluster\], we may think of quantum affine space and quantum tori as cluster algebras where all cluster variables are frozen. In 