Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras

2015/07/16 by Kumjian, Alex, Li, Hui · 1 citation
#22A22 #46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1507.04449

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.

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• Twisted topological correspondences and Cartan subalgebras

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