A CLASSIC MORITA EQUIVALENCE RESULT FOR FELL BUNDLE C*-ALGEBRAS

作者：Ionescu Marius^*; Williams Dana P

来源：Mathematica Scandinavica, 2011, 108(2): 251-263.

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 is an element of G((0)), then C*(G, B) is Morita equivalent to C*(H, C), where C = B vertical bar(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 sigma : 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-1) where C-1 is a Fell bundle over H whose fibres are A/I-A/I-imprimitivity bimodules and I = boolean AND{P : sigma(P) = eH}. Green's result is a special case of our application to bundles over groups.

• 出版日期2011