Amenability and Uniqueness for Groupoids Associated with Inverse Semigroups
| Autor: | LaLonde, Scott M., Milan, David |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff \'{e}tale 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. Comment: 23 pages. This version includes some minor corrections |
| Databáze: | arXiv |
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