An equivalence theorem for reduced Fell bundle C*-algebras

2011/11/24 by Sims, Aidan, Williams, Dana P. · 1 citation
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1111.5753

Abstract

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, proved by Quigg and Spielberg, that Raeburn's symmetric imprimitivity theorem passes through the quotient map to reduced crossed products.

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• Some remarks on Reduced C^*-algebras of semigroup dynamical systems and product systems

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