As we know there are quantum analogue of tori called quantum tori generated by noncommuting operators $(A_1,\dots,A_n)$ with $A _iA_j=A_jA_ie^{2\pi i\alpha}$ where $\alpha$ is a irrational number as a universal $C^*$ algebra and a similar definition of a quantum Euclidean space, can we define a notion of quantum integer space, which completes the circle of classical groups? Also can we have a notion of quantum $p$-adic group? Also can we define some sort of Fourier transform on these spaces, as we can do for quantum tori and quantum Euclidean spaces?