Group actions on labeled graphs and their C*-algebras

TL;DR

This paper explores group actions on labeled graphs, introduces a skew product construction, proves a version of the Gross-Tucker theorem, and applies these concepts to analyze associated C*-algebras and nonabelian duality.

Contribution

It introduces a new framework for group actions on labeled graphs and extends classical theorems to this setting, with applications to C*-algebra theory.

Findings

Established a version of the Gross-Tucker theorem for labeled graphs

Defined a skew product labeled graph construction

Applied results to C*-algebras and nonabelian duality

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 nonabelian duality.