Construction of Simple Modules over the Quantum Affine Space

Abstract

The coordinate ring ${\mathcal{O}}_{\mathbf{q}}({\mathbb{K}}^n)$ of quantum affine space is the $\mathbb{K}$-algebra presented by generators $x_1,\cdots ,x_n$ and relations $x_i{x}_j=q_{ij}{x}_j{x}_i$ for all $i,j$. We construct simple ${\mathcal{O}}_{\mathbf{q}}({\mathbb{K}}^n)$-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.

arXiv comment12 pages