Groupoid algebras as Cuntz-Pimsner algebras

Title
Groupoid algebras as Cuntz-Pimsner algebras
Publication Date
2017-02-23
Author(s)
Rennie, Adam
Robertson, David
( author )
OrcID: https://orcid.org/0000-0002-0425-4775
Email: drober54@une.edu.au
UNE Id une-id:drober54
Sims, Aidan
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Aarhus Universitet, Mathematica Scandinavica
Place of publication
Denmark
DOI
10.7146/math.scand.a-25507
UNE publication id
une:1959.11/31868
Abstract

We show that if G is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle c:G → ℤ, then the reduced C*-algebra of G can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced C*-algebra of the kernel G0 of c. If the full and reduced C*-algebras of G0 coincide, we deduce that the full and reduced C*-algebras of G coincide. We obtain a six-term exact sequence describing the K-theory of C*r (G) in terms of that of C*r (G0).

Link
Citation
Mathematica Scandinavica, 120(1), p. 115-123
ISSN
1903-1807
0025-5521
Start page
115
End page
123

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