n-complete algebras and McKay quivers

ABSTRACT

Let Γⁿ be the cone of an (n−1)-complete algebra over an algebraically closed field k. In this paper, we prove that if the bound quiver $(Q_n,{\rho }_n)$ of Γⁿ is a truncation from the bound McKay quiver $(Q_G,{\rho }_G)$ of a finite subgroup G of GL(n,k), the bound quiver $(Q_{n+1},{\rho }_{n+1})$ of Γⁿ⁺¹, the cone of Γⁿ, is a truncation from the bound McKay quiver $(Q_{\tilde{G}},{\rho }_{\tilde{G}})$ of $\tilde{G}$, where $\tilde{G}\cong G\times {\mathbb{Z}}_m$ for some m∈ℕ.

KEYWORDS:

• Covering spaces
• McKay quiver
• n-complete algebra
• returning arrows

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16G10
• Secondary: 16S34
• 16P90