  Let $Q$ be a finite quiver and $G\subseteq\Aut(\mathbbm{k}Q)$ a finite
abelian group. Assume that $\hat{Q}$ and $\Gamma$ is the generalized Mckay
quiver and the valued graph corresponding to $(Q, G)$ respectively. In this
paper we discuss the relationship between indecomposable
$\hat{Q}$-representations and the root system of Kac-Moody algebra
$\mathfrak{g}(\Gamma)$. Moreover, we may lift $G$ to
$\bar{G}\subseteq\Aut(\mathfrak{g}(\hat{Q}))$ such that $\mathfrak{g}(\Gamma)$
embeds into the fixed point algebra $\mathfrak{g}(\hat{Q})^{\bar{G}}$ and
$\mathfrak{g}(\hat{Q})^{\bar{G}}$ as $\mathfrak{g}(\Gamma)$-module is
integrable.
