Construction of Simple Modules over the Quantum Affine Space

The coordinate ring ${\mathcal{O}}_{\mathbf{q}}({\mathbb{K}}^n)$ of quantum affine space is the $\mathbb{K}$-algebra presented by generators $x_1,\cdots ,x_n$andrelations$x_ix_j=q_{ij}x_jx_i$forall$i,j$\mathrm{.}Weconstructsimple$$\mathcal{O}$_{$\mathbf{q}$}($\mathbb{K}$^n)$-modules in a more general setting where the entries $q_{ij}$ lie in a torsion subgroup of ${\mathbb{K}}^{\ast }$ and show analogous results hold as in single parameter case.