2023/11/21 by Mathias Palmstrøm, Palmstrøm, Mathias
Mathematics · #22A22 #46L05 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2311.12428
openalex publication_date 2023/11/21 · openalex created_date 2023/11/23 · openalex updated_date 2026/07/28
We generalize the ideal completions of countable discrete groups, as introduced by Brown and Guentner, to second countable Hausdorff étale groupoids. Specifically, to every pair consisting of an algebraic ideal in the algebra of bounded Borel functions on the groupoid and a non-empty family of quasi-invariant measures on the unit space, we construct a \rm C^*-algebra in a way which naturally encapsulates the constructions of the full and reduced groupoid \rm C^*-algebras. We investigate the connection between these constructions and the Haagerup property, and use the construction to show the existence of many exotic groupoid \rm C^*-algebras for certain classes of groupoids.