A classic Morita equivalence result for Fell bundle c-algebras

• Autores: Marius Ionescu, Dana P. Williams
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 2, 2011, págs. 251-263
• Idioma: inglés
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• Resumen

  • 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 u∈G(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,CI) where CI 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.