Reduced C*-algebras of Fell bundles over inverse semigroups

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.

References in corpus (1)

• Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

Cited by in corpus (5)

• Aperiodicity: the almost extension property and uniqueness of pseudo-expectations
• Stone duality and quasi-orbit spaces for generalised C*-inclusions
• Amenability and approximation properties for partial actions and Fell bundles
• Positive definiteness and Fell bundles over discrete groups
• Inductive Limits of Noncommutative Cartan Inclusions