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COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  01 June 2009

DAVID PASK ,
JOHN QUIGG  and
AIDAN SIMS
DAVID PASK
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW, 2522, Australia (email: [email protected])
JOHN QUIGG
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona, 85287, USA (email: [email protected])
AIDAN SIMS*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW, 2522, Australia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Consider a projective limit G of finite groups Gn. Fix a compatible family δn of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction δ of G on A. We show that the coaction crossed product of A by δ is isomorphic to a direct limit of the coaction crossed products of A by the δn. If A=C*(Λ) for some k-graph Λ, and if the coactions δn correspond to skew-products of Λ, then we can say more. We prove that the coaction crossed product of C*(Λ) by δ may be realized as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeend’s topological higher-rank graphs and their C*-algebras.

Keywords

C*-algebracoactioncoveringcrossed-productgraph algebrak-graph

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 379 - 398
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research was supported by the ARC.

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