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Two new realizations, denoted $U_{q,x}(\widehat{gl_2})$ and$U(R_{q,x}(\widehat{gl_2}))$ of the trigonometric dynamical quantum affinealgebra $U_{q,\lambda}(\widehat{gl_2})$ are proposed, based onDrinfeld-currents and $RLL$ relations respectively, along with a Heisenbergalgebra $\left\{P,Q\right\}$, with $x=q^{2P}$. Here $P$ plays the role of thedynamical variable $\lambda$ and $Q=\frac{\partial}{\partial P}$. An explicitisomorphism from $U_{q,x}(\widehat{gl_2})$ to $U(R_{q,x}(\widehat{gl_2}))$ isestablished, which is a dynamical extension of the Ding-Frenkel isomorphism of$U_{q}(\widehat{gl_2})$ with $U(R_{q}(\widehat{gl_2}))$ between the Drinfeldrealization and the Reshetikhin-Tian-Shanksy construction of quantum affinealgebras. Hopf algebroid structures and an affine dynamical determinant elementare introduced and it is shown that $U_{q,x}(\widehat{sl_2})$ is isomorphic to$U(R_{q,x}(\widehat{sl_2}))$. The dynamical construction is based on thedegeneration of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ ofJimbo, Konno et al. as the elliptic variable $p \to 0$.

Two Equivalent Realizations of Trigonometric Dynamical Affine Quantum  Group $U_{q,x}(\widehat{sl_2})=U_{q,\lambda}(\widehat{sl_2})$, Drinfeld  Currents and Hopf Algebroid Structures