Abstract
AbstractConsider a projective limitGof finite groupsGn. Fix a compatible familyδnof coactions of theGnon aC*-algebraA. From this data we obtain a coactionδofGonA. We show that the coaction crossed product ofAbyδis isomorphic to a direct limit of the coaction crossed products ofAby theδn. IfA=C*(Λ) for somek-graph Λ, and if the coactionsδncorrespond to skew-products of Λ, then we can say more. We prove that the coaction crossed product ofC*(Λ) byδmay be realized as a full corner of theC*-algebra of a (k+1)-graph. We then explore connections with Yeend’s topological higher-rank graphs and theirC*-algebras.
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