# How to understand the algebra $U_A(Lg)$?

Let $g$ be a complex simple Lie algebra and $Lg = g \otimes \mathbb{C}[t, t^{-1}]$. Let $q$ be a non-zero complex number and $U_q(Lg)$ the quantum loop algebra corresponding to $g$. Let $A = \mathbb{Z}[q, q^{-1}]$. The algebra $U_A(Lg)$ is defined to be a subalgebra of $U_q(Lg)$ such that the natural map $U_A(Lg) \otimes_A \mathbb{Q}(q) \to U_q(Lg)$ is a $\mathbb{Q}(q)$-isomorphism. What do the elements in $U_A(Lg)$ look like? Thank you very much.