Abstract
We investigate recent uniqueness theorems for reduced \(C^*\)-algebras of Hausdorff etale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse semigroup. In order to apply our results to full \(C^*\)-algebras, we also investigate amenability. More specifically, we obtain conditions that guarantee amenability of the universal groupoid for certain classes of inverse semigroups. These conditions also imply the existence of a conditional expectation onto a canonical subalgebra.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have