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We construct an algebra morphism from the elliptic quantum group$E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups inhigher genus'' studied by V. Rubtsov and the first author. This provides anembedding of $E_{\tau,\eta}(sl_2)$ in an algebra ``with central extension''. Inparticular we construct $L^{\pm}$-operators obeying a dynamical version of theReshetikhin--Semenov-Tian-Shansky relations. To do that, we construct thefactorization of a certain twist of the latter algebra, that automaticallysatisfies the ``twisted cocycle condition'' of O. Babelon, D. Bernard and E.Billey, and therefore provides a solution of the dynamical Yang-Baxterequation.Comment: Amslatex file, 43 pages, references adde

Elliptic Quantum Groups $E_{\tau ,\eta } (\mathfrak{s}\mathfrak{l}_2 )$ and Quasi-Hopf Algebras