  In this short note, we compute the classical limits of the quantum toroidal
and the affine Yangian algebras of sl(n) by generalizing our arguments for
gl(1) from arXiv:1404.5240. These results were mentioned as motivation in the
recent study of toroidal algebras by [Feigin-Jimbo-Miwa-Mukhin], while they
played a crucial role in the recent paper arXiv:1512.09109 of the author and
Bershtein. An alternative proof of our key isomorphisms for n>2 was first
established by [Varagnolo-Vasserot]. We also discuss some consequences of these
results.
