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

doi:10.1007/s00233-023-10392-9

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

64 Downloads (Pure)

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.

Original language	English
Pages (from-to)	609-623
Number of pages	15
Journal	Semigroup Forum
Volume	107
Issue number	3
Early online date	17 Oct 2023
DOIs	https://doi.org/10.1007/s00233-023-10392-9
Publication status	Published - Dec 2023

Keywords

Effective groupoid
Local bisection hypothesis
Twisted groupoid C*-algebra

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10.1007/s00233-023-10392-9Licence: CC BY

The local bisection hypothesis for twisted groupoid C*-algebras
Copyright 2023 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 296 KBLicence: CC BY

Cite this

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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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T1 - The local bisection hypothesis for twisted groupoid C*-algebras

AU - Armstrong, Becky

AU - Brown, Jonathan H.

AU - Clark, Lisa Orloff

AU - Courtney, Kristin

AU - Lin, Ying-Fen

AU - McCormick, Kathryn

AU - Ramagge, Jacqui

PY - 2023/12

Y1 - 2023/12

N2 - 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.

AB - 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.

KW - Effective groupoid

KW - Local bisection hypothesis

KW - Twisted groupoid C-algebra

U2 - 10.1007/s00233-023-10392-9

DO - 10.1007/s00233-023-10392-9

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SP - 609

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JO - Semigroup Forum

JF - Semigroup Forum

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ER -

The local bisection hypothesis for twisted groupoid C*-algebras

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