On McKay Quiver and Covering Spaces

Abstract

In this paper, we study the relationship between the McKay quivers of a finite subgroups $G$ of special linear groups general linear groups, via some natural extension and embedding. We show that the McKay quiver of certain extension of a finite subgroup $G$ of $\mathrm{SL}(m,\mathbb{C})$ in $\mathrm{GL}(m,\mathbb{C})$ is a regular covering of the McKay quiver of $G$, and when embedding $G$ in a canonical way into $\mathrm{GL}(m-1,\mathbb{C})$, the new McKay quiver is obtained by adding an arrow from the Nakayama translation of $i$ back to $i$ for each $i$. We also show that certain interesting examples of McKay quivers are obtained in these two ways.

Cited by in corpus (1)

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