GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS

Title & Authors
GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS
Hou, Bo; Yang, Shilin;

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