Recently I've been reading Reshetikhin's lecture note https://arxiv.org/pdf/1010.5031.pdf on integrability of the 6-vertex model. The author defines a complex algebra $C_q(\widehat{\text{SL}}_2)$ as the following.

Consider the $R$-matrix

$$R=\begin{bmatrix} 1 & 0 & 0& 0\\ 0 & f(z) & z^{-1}g(z) & 0\\ 0 & zg(z) & f(z) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$

where

$$ f(z)=\frac{z-z^{-1}}{zq-z^{-1}q^{-1}},\quad g(z)=\frac{q-q^{-1}}{zq-z^{-1}q^{-1}}. $$

Consider the matrix $\mathcal{T}(z)$ which is the generating function for the elements $T^{(k)}_{ij}$

$$\mathcal{T}(z)=\sum^{\infty}_{k=1}T^{(k)}z^{2k}+\begin{bmatrix} T^{(0)}_{11} & T^{(0)}_{12}\\ 0 & T^{(0)}_{22} \end{bmatrix}, $$

where $T^{(k)}_{ij}$ is a matrix element of $T^{(k)}$ for $k\ge 1$. Then the defining relations of $C_q(\widehat{\text{SL}}_2)$ can be written as the following matrix identities with entries in $C_q(\widehat{\text{SL}}_2)$:

$$ R(z)\mathcal{T}(zw)\otimes \mathcal{T}(w)=(1\otimes \mathcal{T}(w))(\mathcal{T}(zw)\otimes 1)R(z)$$

and

$$ \mathcal{T}(qz)_{11}\mathcal{T}(z)_{22}- \mathcal{T}(qz)_{12}\mathcal{T}(z)_{21}=1.$$

I have a feeling that this definition of $C_q(\widehat{\text{SL}_2})$ might have something to do with the affine quantum group $U_q(\widehat{\text{SL}_2})$, but I am not sure at this moment. Are they the same, or if not how are they related to each other?