e define a model $\cH_0(\bfq)$ over $\bbZ$ for the component algebra $\cH_{\tilde{\bbZ}}^{\gamma}(\bfq)\subset \cH_{\tilde{\bbZ}}^{(0)}(\bfq)$. The algebra $\cH_0(\bfq)$ itself will not depend on $\gamma$.  By construction, the $\tilde{\bbZ}[\bfq]$-algebra $\cH_{\tilde{\bbZ}}^{\gamma}(\bfq)$ admits the following presentation: 