Amenability and Uniqueness for Groupoids Associated with Inverse\n Semigroups

2015/11/04 by Scott M. LaLonde, LaLonde, Scott M., David J. Milan +1
Computer Science · Mathematics · #20M18 #46L05 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1511.01517

openalex publication_date 2015/11/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We investigate recent uniqueness theorems for reduced C^*-algebras of\nHausdorff 'etale groupoids in the context of inverse semigroups. In many\ncases the distinguished subalgebra is closely related to the structure of the\ninverse semigroup. In order to apply our results to full C^*-algebras, we\nalso investigate amenability. More specifically, we obtain conditions that\nguarantee amenability of the universal groupoid for certain classes of inverse\nsemigroups. These conditions also imply the existence of a conditional\nexpectation onto a canonical subalgebra.\n

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