- Title
- Groupoid algebras as Cuntz-Pimsner algebras
- Creator
- Rennie, Adam; Robertson, David; Sims, Aidan
- Relation
- Funding BodyARCGrant NumberDP120100507 http://purl.org/au-research/grants/arc/DP120100507
- Relation
- Mathematica Scandinavica Vol. 120, Issue 1, p. 115-123
- Publisher Link
- http://dx.doi.org/10.7146/math.scand.a-25507
- Publisher
- Aarhus Universitet, Mathematica Scandinavica
- Resource Type
- journal article
- Date
- 2017
- Description
- 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). - Subject
- Cuntz-Pimsner algebra; groupoid algebras
- Identifier
- http://hdl.handle.net/1959.13/1385590
- Identifier
- uon:32254
- Identifier
- ISSN:0025-5521
- Language
- eng
- Full Text
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