A classic Morita equivalence result for Fell bundle C^*-algebras - Ionescu, Marius; Dilliams, Dana P. (MATHEMATICA SCANDINAVICA, 2011)
We show how to extend a classic Morita Equivalence Result of Green’s to the C^*-algebras of Fell bundles over transitive groupoids. Specifically, we show that if p:B→ G is a saturated Fell bundle over a transitive groupoid G with stability group H=G(u) at uG^(0), then C^* (G,B) is Morita equivalent to C^*(H,C), where C=B_| H. As an application, we show that if p:B→ G is a Fell bundle over a group G and if there is a continuous G-equivariant map σ: Prim A→ G/H, where A=B(e) is the C^*-algebra of B and H is a closed subgroup, then C^*(G,B) is Morita equivalent to C^* (H,C^I) where C^I is a Fell bundle over H whose fibres are A/I-A/I-imprimitivity bimodules and I={ P:σ(P)=eH}. Green’s result is a special case of our application to bundles over groups.