Rennie, Adam; Robertson, David; Sims, Aidan

Author(s)

Rennie, Adam

Robertson, David

Sims, Aidan

Publication Date

2017-02-23

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).

Citation

Mathematica Scandinavica, 120(1), p. 115-123

ISSN

1903-1807

0025-5521

Link

https://hdl.handle.net/1959.11/31868

Publisher

Aarhus Universitet, Mathematica Scandinavica

Title

Groupoid algebras as Cuntz-Pimsner algebras

Type of document

Journal Article

Entity Type

Publication

Author(s)	Rennie, Adam Robertson, David Sims, Aidan
Publication Date	2017-02-23
Abstract	<p>We show that if <i>G</i> is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle <i>c</i>:<i>G</i> → ℤ, then the reduced <i>C</i>-algebra of <i>G</i> can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced <i>C</i>-algebra of the kernel <i>G</i><sub>0</sub> of <i>c</i>. If the full and reduced <i>C</i>-algebras of <i>G</i><sub>0</sub> coincide, we deduce that the full and reduced <i>C</i>-algebras of <i>G</i> coincide. We obtain a six-term exact sequence describing the <i>K</i>-theory of <i>C</i><sub>r</sub> (<i>G</i>) in terms of that of <i>C</i><sub>r</sub> (<i>G</i><sub>0</sub>).</p>
Citation	Mathematica Scandinavica, 120(1), p. 115-123
ISSN	1903-1807 0025-5521
Link	https://hdl.handle.net/1959.11/31868
Publisher	Aarhus Universitet, Mathematica Scandinavica
Title	Groupoid algebras as Cuntz-Pimsner algebras
Type of document	Journal Article
Entity Type	Publication

Groupoid algebras as Cuntz-Pimsner algebras

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