Does Sklyanin algebra (which is an elliptic extension of the quantum group) admit a bialgebra structure or even Hopf algebraic structure? Or is it proved that it is impossible to have such a structure? 

Note that the algebra is defined as four generators $S_0, S_{\alpha = 1,2,3}$ and
\begin{equation}
\begin{aligned}
& \{ S_0, S_{\alpha} \} = 2 J_{\beta \gamma} S_{\beta} S_{\gamma}\\[0.5em]
& \{ S_{\alpha}, S_{\beta} \} = -2 S_0 S_{\gamma}
\end{aligned}
\end{equation}
where $(\alpha, \beta, \gamma)$ is the cyclic permutation of $1,2,3$.