An equivalence theorem for reduced Fell bundle C*-algebras

Details An equivalence theorem for reduced Fell bundle C*-algebras An equivalence theorem for reduced Fell bundle C*-algebras

2011-11-24

arxiv.org/abs/1111.5753v1

Mathematics

Operator Algebras

17 pages

Scientific paper

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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