# Equivariant Dimensions of Graph C*-algebras

## TL;DR

This paper investigates the local-triviality dimensions of gauge actions on various graph C*-algebras, providing characterizations for finite acyclic graphs and cycles, and analyzing examples like Toeplitz, Cuntz, and q-deformed spheres.

## Contribution

It introduces a detailed study of local-triviality dimensions in gauge actions on graph C*-algebras, including new characterizations and analysis of key examples.

## Key findings

- Finiteness of local-triviality dimensions characterized for finite acyclic graphs.
- Finiteness characterized for finite cycle graphs.
- Analysis of gauge actions on Toeplitz, Cuntz, and q-deformed spheres.

## Abstract

We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and finite cycles, we characterize the finiteness of these dimensions, and we further study the gauge actions on many examples of graph $C^*$-algebras. These include the Toeplitz algebra, Cuntz algebras, and $q$-deformed spheres.