Coverings of skew products and crossed products by coactions

Authors

David A. Pask, dpask@uow.edu.auFollow
John Quigg, Arizona State University
Aidan Sims, University of WollongongFollow

RIS ID

29370

Publication Details

Pask, D., Quigg, J. & Sims, A. (2009). Coverings of skew products and crossed products by coactions. Australian Mathematical Society Journal, 86 (3), 379-398.

Abstract

Consider a projective limit G of finite groups G_n. Fix a compatible family δⁿ of coactions of the G_n 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.