Abstract. Let Q be a finite quiver and G ⊆ Aut( Q) a finite abelian group. Assume that Q and Γ are the generalized Mckay quiver and the valued graph corresponding to (Q, G) respectively. In this paper we discuss the relationship between indecomposable Q-representations and the root system of Kac-Moody algebra g(Γ). Moreover, we may lift G to G ⊆ Aut(g( Q)) such that g(Γ) embeds into the fixed point algebra g( Q) G and g( Q) G as a g(Γ)-module is integrable.

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