The component quiver of a self-injective artin algebra
Volume 122 / 2011
Colloquium Mathematicum 122 (2011), 233-239
MSC: 16D50, 16G10, 16G70.
DOI: 10.4064/cm122-2-8
Abstract
We prove that the component quiver ${\mit\Sigma }_A$ of a connected self-injective artin algebra $A$ of infinite representation type is fully cyclic, that is, every finite set of components of the Auslander–Reiten quiver ${\mit\Gamma }_A$ of $A$ lies on a common oriented cycle in ${\mit \Sigma }_A$.
