Classical limits of quantum toroidal and affine Yangian algebras

In this short article, we compute the classical limits of the quantum toroidal and affine Yangian algebras of ${\mathfrak{sl}}_n$ by generalizing our arguments for ${\mathfrak{gl}}_1$ from 7] (an alternative proof for $n>2$ is given in 10]). We also discuss some consequences of these results.