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arXiv · 2307.13814

The local bisection hypothesis for twisted groupoid C*-algebras

Becky Armstrong·Jonathan H. Brown·Lisa Orloff Clark·Kristin Courtney·Ying-Fen Lin·Kathryn McCormick·Jacqui Ramagge
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Abstract

In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid $G$ being effective. One of these conditions is that $G$ satisfies the "C*-algebraic local bisection hypothesis"; that is, that every normaliser in the reduced twisted groupoid C*-algebra is supported on an open bisection. The semigroup of normalisers plays a fundamental role in our proof, as does the semigroup of normalisers in cyclic group C*-algebras.

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Becky Armstrong, Jonathan H. Brown, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge. 2023-10-23. The local bisection hypothesis for twisted groupoid C*-algebras. https://doi.org/10.1007/s00233-023-10392-9

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