TWISTED TOPOLOGICAL GRAPH ALGEBRAS ARE TWISTED GROUPOID C*-ALGEBRAS

摘要

In Twisted topological graph algebras, to appear in Houston J. Math., 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-1. 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.