[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2015.52.2.239

GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS

Hou, Bo (School of Mathematics and Statistics Henan University)
Yang, Shilin (College of Applied Science Beijing University of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 239-268 More about this Journal

Abstract

Let Q be a finite quiver and $G{\subseteq}Aut(\mathbb{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and ${\Gamma}$ are 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 $g({\Gamma})$ . Moreover, we may lift G to $\bar{G}{\subseteq}Aut(g(\hat{Q}))$ such that $g({\Gamma})$ embeds into the fixed point algebra $g(\hat{Q})^{\bar{G}}$ and $g(\hat{Q})^{\bar{G}}$ as a $g({\Gamma})$ -module is integrable.

Keywords

generalized McKay quiver; representation of quiver; root system; Kac-Moody algebra;

Citations & Related Records

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