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Groupoid algebras as Cuntz-Pimsner algebras

journal contribution
posted on 2024-11-16, 04:46 authored by Adam RennieAdam Rennie, David Robertson, Aidan SimsAidan Sims
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).

Funding

Invariants for dynamics via operator algebras

Australian Research Council

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History

Citation

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

Journal title

Mathematica Scandinavica

Volume

120

Issue

1

Pagination

115-123

Language

English

RIS ID

113959

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