For Dynkin quivers, we find the Laurent polynomials $\widetilde{ X}_{ a, c}^{ b}(v)$ and use $\widetilde{ X}_{ a, c}^{ b}(v)$ to construct the Hall algebra $\hc_v(\cc(\cp))$ over $\mz[v, v^{ -1}]$, where $\widetilde{ X}_{ a, c}^{ b}(|\mf_q|)$'s are structure constants used by Bridgeland. The Laurent polynomials $\widetilde{ X}_{ a, c}^{ b}(v)$ are explicitly given in $A_1$ case. As an application, we obtain the full quantum groups $U_t(\sg)$ associated to the Dynkin quivers for arbitrary $t\not=0,\pm1$.
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