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Groupoid algebras as Cuntz-Pimsner algebras |
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Aarhus Universitet, Mathematica Scandinavica |
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10.7146/math.scand.a-25507 |
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| 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). |
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Mathematica Scandinavica, 120(1), p. 115-123 |
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