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

TL;DR

This paper demonstrates that for the algebra , the standard coproducts of Yangians and quantum affine algebras can be factored through their truncated quotients, providing explicit formulas for these coproducts.

Contribution

It establishes the factorization of coproducts through truncated quotients for , a novel result in the study of quantum affine algebras and Yangians.

Findings

Coproducts factorize through truncated quotients for .

Explicit formulas for coproducts of truncation series.

Results specific to  case.

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.