Let $g$ be a Lie algebra. Then we have a corresponding affine Lie algebra \begin{align} \hat{g} = g \otimes \mathbb{C}[t,t^{-1}] \oplus \mathbb{C}c, \end{align} where $c$ is the central element.

The corresponding quantum affine algebra $U_q(\hat{g})$ is generated by $C^{\pm 1/2}$, $k_i^{\pm 1}$, $h_{i,m}$, $i \in I, m \in \mathbb{Z}-\{0\}$, $x_{i,m}^{\pm}$, $i \in I, m \in \mathbb{Z}$, where $C$ is some central element.

What is the relation between $c$ and $C$? Thank you very much.


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