Reduced C*-algebras of Fell bundles over inverse semigroups |
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Authors: | Alcides Buss Ruy Exel Ralf Meyer |
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Institution: | 1.Departamento de Matemática,Universidade Federal de Santa Catarina,Florianópolis-SC,Brazil;2.Mathematisches Institut,Georg-August-Universit?t G?ttingen,G?ttingen,Germany |
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Abstract: | We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced C*-algebra for an inverse semigroup action on a groupoid by partial equivalences coincides with the reduced groupoid C*-algebra of the transformation groupoid, giving both positive results and counterexamples. |
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