Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras

TL;DR

This paper demonstrates that twisted topological graph C*-algebras can be represented as twisted groupoid C*-algebras, linking graph algebra constructions with groupoid models through boundary path groupoids.

Contribution

It establishes an isomorphism between twisted topological graph C*-algebras and twisted groupoid C*-algebras using Renault-Deaconu groupoids and boundary path spaces.

Findings

Shows the isomorphism between twisted topological graph algebras and twisted groupoid algebras

Uses Renault-Deaconu groupoids and boundary path spaces in the construction

Provides a new perspective on the structure of twisted graph algebras

Abstract

The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the compactly supported continuous sections of L. We prove that the resulting C*-algebra is isomorphic to a twisted groupoid C*-algebra where the underlying groupoid is the Renault-Deaconu groupoid of the topological graph with Yeend's boundary path space as its unit space.