Compatibility between truncation and coproducts for quantum affine algebra and Yangian of $\mathfrak{sl}_2(\mathbb{C})$

Abstract

We prove that the standard Drinfeld-Jimbo coproducts for Yangians and quantum affine algebras factorize through their truncated quotients in the case of $\mathfrak{sl}_2(\mathbb{C})$. As an auxiliary result, we give formulas for the coproduct of the truncation series in both cases.