C*-dynamical systems associated to Graph C*-Algebras

TL;DR

This paper investigates the ideal structure of graph C*-algebras by analyzing their realization as Stacey crossed products, linking algebraic properties to associated C*-dynamical systems.

Contribution

It introduces a novel approach to study graph C*-algebras through their characterization as Stacey crossed products, providing new insights into their ideal properties.

Findings

Characterization of graph C*-algebras as Stacey crossed products.

Analysis of ideal properties via associated C*-dynamical systems.

Enhanced understanding of the algebraic structure of graph C*-algebras.

Abstract

We use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^\gamma \times_{\beta_E} N, to study its ideal properties in terms of the (non-classical) C*-dynamical system (C*(E)^\gamma, \beta_E)