z_0\mapsto U^0$, and it is an isomorphism. In particular, $\cA_0(\bfq)$ is a [*commutative*]{} subalgebra of $\cH_0(\bfq)$. The isomorphism \[H0VSHgamma\] identifies $\cA_0(\bfq)\otimes_{\bbZ}\tilde{\bbZ}$ with $\cA_{\tilde{\bbZ}}^{\gamma}(\bfq)$. Moreover, permuting $