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Groupoid algebras as Cuntz-Pimsner algebras

Journal Article


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 Cr ∗(G) in terms of that of Cr ∗(G0).

Publication Date


  • 2017

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2017). Groupoid algebras as Cuntz-Pimsner algebras. Mathematica Scandinavica, 120 (1), 115-123.

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/201

Number Of Pages


  • 8

Start Page


  • 115

End Page


  • 123

Volume


  • 120

Issue


  • 1

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 Cr ∗(G) in terms of that of Cr ∗(G0).

Publication Date


  • 2017

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2017). Groupoid algebras as Cuntz-Pimsner algebras. Mathematica Scandinavica, 120 (1), 115-123.

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/201

Number Of Pages


  • 8

Start Page


  • 115

End Page


  • 123

Volume


  • 120

Issue


  • 1