  We define an algebra $\mathcal{U}_0$ using a simplified set of generators for
the quantum toroidal algebra $U_q(sl_{n+1}, tor)$ and show that there exists an
epimorphism from $\mathcal{U}_0$ to $U_q(sl_{n+1}, tor)$. We derive a closed
formula of the comultiplication on the generators of $\mathcal{U}_0$ that
extends that of the quantum affine algebra $U_q(\hat{sl}_{n+1})$. As a
consequence, we show that $\mathcal{U}_0$ is a Hopf algebra for $n=1, 2$ and
give conjectural formulas in the general case. We further show that
$\mathcal{U}_0$ is isomorphic to a double algebra.
