Coverings of skew-products and crossed products by coactions

David Pask; John Quigg; Aidan Sims

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arXiv · 0706.0362

Coverings of skew-products and crossed products by coactions

David Pask·John Quigg·Aidan Sims

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Abstract

Consider a projective limit G of finite groups G_n. Fix a compatible family δ^n of coactions of the G_n on a C*-algebra A. From this data we obtain a coaction δof G on A. We show that the coaction crossed product of A by δis isomorphic to a direct limit of the coaction crossed products of A by the δ^n. If A = C*(Λ) for some k-graph Λ, and if the coactions δ^n correspond to skew-products of Λ, then we can say more. We prove that the coaction crossed-product of C*(Λ) by δmay be realised 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.

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BibTeX RIS

David Pask, John Quigg, Aidan Sims. 2008-05-14. Coverings of skew-products and crossed products by coactions. https://arxiv.org/abs/0706.0362

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