GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS
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Let Q be a finite quiver and G ⊆ Aut(kQ) a finite abelian group. Assume that Q＾ and T are the generalized Mckay quiver and the valued graph corresponding to (Q,G) respectively. In this paper we dis- cuss the relationship between indecomposable Q＾ -representations and the root system of Kac-Moody algebra g(T). Moreover, we may lift G to G ⊆ Aut(g(Q＾)) such that g(T) embeds into the fixed point algebra g(Q＾)G and g(Q＾)G as a g(T)-module is integrable.
Abstract
Let Q be a finite quiver and G ⊆ Aut(kQ) a finite abelian group. Assume that Q＾ and T are the generalized Mckay quiver and the valued graph corresponding to (Q,G) respectively. In this paper we dis- cuss the relationship between indecomposable Q＾ -representations and the root system of Kac-Moody algebra g(T). Moreover, we may lift G to G ⊆ Aut(g(Q＾)) such that g(T) embeds into the fixed point algebra g(Q＾)G and g(Q＾)G as a g(T)-module is integrable.
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