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Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras

Published online by Cambridge University Press:  19 September 2008

Baruch Solel
Baruch Solel
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
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Abstract

For a 1-cocycle c on a principal r-discrete groupoid G, that vanishes only on the unit space of G, we show that the asymptotic range of c, , is an invariant for the total order c−1([0, ∞]). It follows that is also an invariant (with respect to isometric isomorphisms) of the triangular analytic algebra supported on c−1([0, ∞]). We also prove that if and only if the analytic algebra has a certain maximality property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992 , pp. 341 - 358
Copyright
Copyright © Cambridge University Press 1992

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