Group actions on labeled graphs and their $C^{*}$-algebras

Abstract

We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross–Tucker theorem for labeled graphs. We then apply these results to the $C^{*}$-algebra associated to a labeled graph and provide some applications in non-Abelian duality.