  We explicitly find the spectrum of the operators $M^{rs}$ and
$\widetilde{M}^{rs}$, which specify the star-product in the matter and ghost
sectors correspondingly. Further we derive the diagonal representation for the
3-string vertices. Using this representation we identify the appearing Moyal
structures in the matter sector. In addition to the continuous
non-commutativity parameter $\theta(\kappa)$ found in hep-th/0202087 we find
the discrete non-commutativity parametrized by $\theta_{\xi}$.
