Limits of groupoid C*-algebras arising from open covers

Details Limits of groupoid C*-algebras arising from open covers Limits of groupoid C*-algebras arising from open covers

2008-03-16

arxiv.org/abs/0803.2374v1

Mathematics

Operator Algebras

Scientific paper

I. Raeburn and J. Taylor have constructed continuous-trace C*-algebras with a prescribed Dixmier-Douady class, which also depend on the choice of an open cover of the spectrum. We study the asymptotic behavior of these algebras with respect to certain refinements of the cover and appropriate extension of cocycles. This leads to the analysis of a limit groupoid G and a cocycle \sigma, and the algebra C*(G, \sigma) may be regarded as a generalized direct limit of the Raeburn-Taylor algebras. As a special case, all UHF C*-algebras arise from this limit construction.

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